-I 


DIELECTRIC  PHENOMENA 

IN 

HIGH  VOLTAGE  ENGINEERING 


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DIELECTKIC  PHENOMENA 

IN 

HIGH  VOLTAGE  ENGINEERING 


BY 


F.  W.  PEEK,  JR. 
If 


SECOND  EDITION 


McGRAW-HILL  BOOK  COMPANY,  INC. 

NEW  YORK:    239  WEST  39TH  STREET 

LONDON:    6  &  8  BOUVERIE  ST.,  E.  C.  4 

1920 


IJi-0 

Engineering 
Library 


COPYRIGHT,  1915,  1920,  BY  THE 
MCGRAW-HILL  BOOK  COMPANY,  INC.      Jr 


THK     M  A  I»  1.  K     1»HEBS 


PREFACE  TO  SECOND  EDITION 

In  this  edition  the  text  has  been  very  carefully  reviewed  and 
typographical  and  other  errors  corrected.  It  has  not  been 
found  necessary  to  make  any  fundamental  changes.  During 
the  last  five  years  important  investigations  on  transient  and 
lightning  voltages,  high  voltage  d.  c.  etc.,  have  been  made. 
Data  on  these  and  other  recent  investigations  have  been 
added  to  the  text  and  the  appendix. 

F.  W.  PEEK,  JR. 

PlTTSFIELD,    MASS. 

July,  1920. 


434559 


PREFACE  TO  FIRST  EDITION 

It  is  the  object  of  the  author  to  give  in  this  book  the  properties 
of  gaseous,  liquid  and  solid  insulations,  and  methods  of  utilizing 
these  properties  to  the  best  advantage  in  the  problems  of  high- 
voltage  engineering.  Such  problems  require  a  knowledge,  not 
only  of  the  laws  and  mechanism  of  breakdown  of  dielectrics  as 
determined  by  experiment,  but  also  a  simple  working  knowledge 
of  the  dielectric  circuit. 

Methods  that  have  proved  useful  in  designing  apparatus, 
transmission  lines,  insulators,  bushings,  etc.,  are  discussed  and 
illustrated  by  practical  application.  In  addition,  such  subjects 
as  the  manner  of  making  extensive  engineering  investigations 
and  of  reducing  data,  the  measurement  of  high  voltages,  the 
effects  of  impulse  and  high-frequency  voltages,  methods  of  draw- 
ing dielectric  fields,  outline  of  modern  theory,  various  dielectric 
phenomena,  etc.,  are  considered.  In  all  cases  where  laws  and 
discussions  of  dielectric  phenomena  are  given,  it  has  been  thought 
best  to  accompany  these  with  experimental  data. 

Much  original  work  is  given,  as  well  as  reference  to  other  in- 
vestigations. The  author's  extensive  research  was  made  possible 
by  facilities  afforded  by  the  Consulting  Engineering  Department 
of  the  General  Electric  Company,  for  which  acknowledgment 
is  made.  Thanks  are  due  Mr.  H.  K.  Humphrey,  and  others,  who 
have  greatly  assisted  in  the  experiments  and  calculations. 

F.  W.  P.,  JR. 

SCHENECTADY,  N.  Y., 

April,  1915. 


VI' 


CONTENTS 

PAGE 

PREFACE v 

DIELECTRIC  UNITS xi 

TABLE  OF  SYMBOLS , xiii 

CHAPTER  I 

INTRODUCTION 1 

General  discussion  of  energy  transfer — Experimental  plots  of  di- 
electric and  magnetic  fields — Analogy  between  magnetic  and 
dielectric  fields — Analogy  with  Hooke  s  Law. 

CHAPTER  II 

THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT 8 

(Mathematical  Consideration) 

General  treatment  of  the  dielectric  field  and  dielectric  circuit  with 
discussion  of  principles  used — Parallel  planes — Field  between ;  per- 
mittance, etc. — Concentric  cylinders — Permittance  or  capacity; 
flux  density  and  gradient — Parallel  wires — Principles  used  in  super- 
position of  fields;  determination  of  resultant  fields;  equation  of 
equipotential  surfaces,  lines  of  force  and  flux  density;  permittance; 
gradient  and  equigradient  surfaces — Concentric  spheres — Spheres 
—Two  small  equal  spheres,  field  of,  and  permittance;  two  large 
equal  spheres,  gradient,  permittance — Conditions  for  spark-over 
and  local  breakdown  or  corona — Collected  formulae  for  common 
electrodes — Combinations  of  dielectrics  of  different  permittivities 
— Dielectric  flux  refraction — Dielectric  in  series — Dielectric  in 
multiple — Flux  control — Imperfect  electric  elastivity  or  absorption 
in  dielectrics;  dielectric  hysteresis. 

CHAPTER  III 

VISUAL  CORONA 38 

General  Summary  and  Discussion — Appearance — Chemical  action 
— A.  C.  and  D.  C.  spacing  and  size  of  conductor — Laws  of  visual 
corona  formation — Theory  of  corona — Electron  theory — Air  films 
at  small  spacings — Air  density — Measuring  voltage  by  corona — 
Conductor  material,  cables,  oil  and  water  on  the  conductors, 
humidity.  lonization — Wave  shape,  current  in  wire. 
Experimental  Study  and  Method  of  Reducing  Experimental  Data — 
Tests  showing  the  effects  of  size  and  spacing  of  conductors — Air 
density — Temperature — Barometric  pressure — Strength  of  air 
films — Effect  of  frequency — Conductor  material,  oil,  water,  dirt, 
humidity — lonization — Current  in  wire — Stranded  conductors — 
Split  conductors. 

Photographic  and  Stroboscopic  Study — Positive  and  negative  corona 
— Corona  at  different  voltages — Thickness  of  corona — Oscillograms 
of  corona  current,  etc. 

vii 


viii  CONTENTS 

CHAPTER  IV 

PAGE 

(SPARK-OVER  . 79 
Definition — Condition  for  spark-over  or  corona — Spark-over  be- 
tween parallel  wires,  wet  and  dry — Measurements  of  and  method  of 
calculating — Wires  in  a  cylinder — Needle  gap — Sphere  gap — 
Effect  of  barometric  pressure,  temperature,  humidity,  moisture  and 
rain  on  spark -over;  measurement  of  voltage  by  spheres;  calculation 
of  curves;  precautions  in  testing — Rupturing  energy  and  dielectric 
spark  lag — Law  of  spark-over,  effect  of  high  frequency,  oscillatory, 
and  impulse  voltages  on  spark-over,  and  method  of  measuring  such 
voltages — Insulators  and  bushings — Spark-over  of;  effect  of  alti- 
tude, etc. 

CHAPTER  V 

CORONA  Loss 117 

Method  of  making  a  large  engineering  investigation — Method  of 
reducing  data — The  quadratic  law — Loss  on  very  small  conductors 
— Effect  of  frequency,  size  of  conductor  and  spacing;  conductor 
material  and  surfaces;  air  density  and  humidity — The  disruptive 
critical  voltage — Loss  near  the  disruptive  critical  voltage;  the 
probability  law — Loss  during  storm — Loss  at  very  high  frequency. 

CHAPTER  VI 

CORONA  AND  SPARK-OVER  IN  OIL  AND  LIQUID  INSULATIONS 153 

Liquids  used  for  insulating — Physical  characteristics  of  transformer 
oil — Spark-over  with  different  electrodes;  effect  of  moisture;  tem- 
perature— Corona  in  oil — Law  of  spark-over  and  corona  in  oil — 
Spark -over  of  wires,  plates  and  cylinders — Resistivity  of  oil — Dis- 
ruptive energy — Oil  films — Transient  voltages — Barriers — Com- 
parison of  high  frequency — 60  —  and  impulse  arc  over. 

CHAPTER  VII 

SOLID  INSULATION 166 

Solids  used  for  insulation — Dielectric  loss — Insulation  resistance 
and  dielectric  strength — Rupturing  gradient — Methods  of  testing 
— Law  of  strength  vs.  thickness — Solid  vs.  laminated  insulations — 
Effect  of  area  of  electrodes — Impulse  voltages  and  high  frequency 
— Cumulative  effect  of  over-voltages  of  steep  wave  front — Law  of 
strength  vs.  time  of  application — Permittivity  of  insulating 
materials — Energy  loss  in  insulations  at  high  and  low  frequency — 
Operating  temperatures  of  insulation — Surface  leakage — Solid 
insulating  barriers  in  oil — Impregnation — Mechanical — Direct 
current — Complete  data  on  permittivity,  dielectric  strength  with 
time,  thickness,  etc. 

CHAPTER  VIII 

THE  ELECTRON  THEORY 192 

Review  of  and  example  of  practical  application. 


CONTENTS  ix 

CHAPTER  IX 

PAGE 

PRACTICAL  CORONA  CALCULATION  FOR  TRANSMISSION  LINES 199 

Corona  and  summary  of  various  factors  affecting  it — Practical 
corona  formulae  and  their  application  with  problems  to  illustrate — 
Safe  and  economical  voltages — Methods  of  increasing  size  of  con- 
ductors— Conductors  not  symmetrically  spaced — Voltage  change 
along  line — Agreement  of  calculated  losses  and  measured  losses  on 
commercial  transmission  lines — The  corona  limit  of  high-voltage 
transmission,  with  working  tables  and  curves. 

CHAPTER  X 

PRACTICAL  CONSIDERATIONS  IN  THE  DESIGN  OF  APPARATUS  WHERE 
SOLID,  LIQUID  AND  GASEOUS  INSULATIONS  ENTER  IN  COMBINATION  .  213 
Breakdown  caused  by  addition  of  stronger  insulation — Corona  on 
generator  coils — Corona  in  entrance  bushings — Grade'd  cable — 
Transformer  bushing,  oil-filled  bushings,  condenser  type  bushing — 
Dielectric  field  control  by  metal  guard  rings,  shields,  etc. — High 
frequency — Dielectric  fields — Methods  of  plotting,  lines  of  force, 
•  equipotential  surfaces,  equigradient  surfaces — Dielectric  fields  in 
three  dimensions,  experimental  determination  of  dielectric  fields — 
Effect  of  ground  on  the  dielectric  field  between  wires — Three- 
phase  dielectric  fields  with  flat  and  triangular  spacing  of  con- 
ductors— Occluded  air  in  insulations — Examples  of  calculations  of 
spark-over  between  wet  wires,  of  sphere  curves,  of  breakdown  of 
insulation  for  transient  voltages,  of  strength  of  porcelain,  of  energy 
loss  in  insulation,  etc. 

CHAPTER  XI 

COMPLETE  DATA  APPENDIX 238 

Measured  data  on  corona  loss. 

INDEX 257 


DIELECTRIC   UNITS 

Electromotive  force,  volts  e       volts. 

Gradient  g  =  -  volts/cm. 

Permittance  or  capacitance  or  kKA  .  kA   „ 

C  =  -  -    -  =  8.84          10~14  farads, 
capacity.  x  x 

Permittivity  or  specific  capacity 

relative  k  (k  =  1  for  air) 

109 
absolute  (air)  K  =  -^—^  =  8.84  X  10~H  farad  cm.  cube. 

Elastance  S  —  -^ 

Elastivity  a  =  l/k 

Flux,  displacement  ^  =  Ce  =  -~  coulombs  (or  lines  of  force). 

Flux  density,  D  =  kKg  flux  or  displacement  per  cm.2 

Intensity  F       (unit  not  used  in  text). 

Ce2 
Stored  energy  wc  =  -«-  joules. 

Energy  density  w0  =  -^  joules  per  cm.  cube. 

d\L  de 

Permittance  or  capacity  current      ic  —  ~ji  —  C  ,    amps. 

Permittance  or  capacity  current     ic  =  2-irfCe  amps,  for  sine  wave. 

1111 
Permittance  in  series  7,  =  -^ — (-  ~n — r  TT 

C          C  1  U  2          v^  3 

Elastance  in  series  S  =  Si  +  S2  +  S3 

Permittance  in  multiple  C  =  Ci  +  C2  +  C3 

1111 

Elastance  in  multiple  ^  =  o"  +  o~  +  o" 

v  =  velocity  of  light  =  3  X  1010  cm.  per  sec. 
x=  spacing  cm.     A  =  area  in  sq.  cm. 

NOTE. — For  non-uniform  fields  e,  x,  etc.    are  measured  over  very  small  distances  and  be- 
come de,  dx,  etc.     Then  the  gradient  at  any  point  is  o=  , ;-,  etc. 


XI 


TABLE  OF  SYMBOLS 

The  following  is  a  list  of  the  principal  symbols  used.  The  use  given 
first  is  the  most  general  one.  The  meaning  is  always  given  hi  the  text  for 
each  individual  case. 

A  area  in  square  cm.,  constant. 
A'lA'z  flux  foci  or  flux  centers. 
a  distance,  constant. 

b  barometric  pressure  in  cm.,  constant,  distance. 
C  permittance  or  capacity. 
Cr,r2  permittance  between  points  r\  r2. 
Cn  permittance  to  neutral. 
c  constant,  distance. 
D  dielectric  flux  density. 
d  distance,  constant. 
e  voltage. 

en  voltage  to  neutral. 
enr2  voltage  between  points  r\  r2. 
ep  voltage  to  point  p. 
ev  visual  critical  corona  voltage. 
e0  disruptive  critical  corona  voltage. 
ed  disruptive  critical  corona  voltage  for  small  wires. 
ea  spark-over  voltage. 
/  frequency. 

/,/!,/„  coefficients  used  in  reducing  average  gradient  to  maxi- 
mum— see  page  28. 

F  constant  (sometimes  used  for  dielectric  field  intensity). 
g,  G  gradient. 

g  gradient  volts  per  cm.  or  kilovolts  per  cm. 
g  gradient  volts  per  mm.  for  solid  insulations. 
gv  visual  critical  gradient. 
g0  disruptive  critical  gradient. 
gd  disruptive  critical  gradient  for  small  wires. 
Qmax  maximum  gradient — see  note  below. 
gs  spark  gradient. 
ga  gradient  at  point  a. 
h  constant,  height. 
i  current  amperes. 
K  dielectric  constant  for  air 

109 

K  =  -    -  =  8.84  X  10~14  farads  per  cm.  cube. 
4-n-y2 

k  relative  permittivity  (k  =  1  for  air). 
L  inductance. 
I  length,  thickness 

xiii 


xiv  TABLE  OF  SYMBOLS 

M  constant. 

m  ordinate  of  center  of  line  of  force, 
m  mass. 

mv,  m0  irregularity  factor  of  conductor  surface. 
N  neutral  plane. 
n  number. 
0  center  point. 
P  point. 
p  power  loss. 
q  constant. 

r  radius  of  wires  or  cables. 
R  radius  of  spheres,  of  outer  cylinder. 
r  resistance. 

S,  s  spacing  between  conductor  centers. 
S'  distance  between  flux  foci. 

5  elastance — see  page  11. 
t  temperature,  thickness. 

T  time. 

v  velocity  of  light  in  cm. /sec.  =  3  X  1010. 
v  velocity. 

Wi  magnetic  stored  energy. 
wc  dielectric  stored  energy. 
w  weight. 

X,  x  cm.  spacing  between  conductor  surfaces,  thickness,  co- 
ordinate of  a  point. 
x\,  Xz  distance. 

y  coordinate  of  point. 

z  distance  from  the  center  of  a  conductor  or  an  equipo- 

tential  circle  to  flux  foci. 
a  angle,  constant. 
/3  constant. 

6  relative  air  density. 
AS  difference  of  two  sums. 

€  base  of  natural  log. 

^  dielectric  displacement  or  dielectric  flux. 
*  magnetic  flux. 
<f>  angle,  function. 
0  angle. 
a  elastivity. 
S  sum. 
SS  sum  of  two  sums. 

to  resistance, 
mm.  millimeter, 
cm.  centimeter.  t 

=  approximately  equal  to. 

Note  that  voltages  in  measured  data  are  often  given  to  neutral;  in  such 
cases  the  single  phase  line  to  line  voltages  are  twice  (2),  and  the  three  phase 
(symmetrical)  \/3  times,  these  values. 


TABLE  OF  SYMBOLS  XV 

Permittances  or  capacities  are  also  frequently  given  to  neutral  because 
it  is  a  great  convenience  in  making  calculations. 

The  subscript  max.  is  often  used  to  distinguish  between  the  maximum  and 
root  mean  square  or  effective.  This  is  done  because  insulation  breakdown 
generally  depends  upon  the  maximum  point  of  the  wave.  Such  voltages 
may  be  reduced  to  effective  sine  wave  by  dividing  by  \/2.  Sometimes 
when  the  maximum  gradient  is  referred  to  it  means  the  gradient  at  the 
point  in  the  field  where  the  stress  is  a  maximum.  These  references  are  made 
clear  in  the  text  for  each  individual  case. 

Tests  were  made  on  single-phase  lines  unless  otherwise  noted. 

Views  or  theories  advanced  by  the  author  are  always  accompanied  by 
sufficient  experimental  data  so  that  the  reader  may  form  conclusions 
independently. 


DIELECTRIC  PHENOMENA 

CHAPTER  I 
INTRODUCTION 

It  is  our  work  as  engineers  to  devise  means  of  transmitting 
energy  electrically,  from  one  point  to  another  point,  and  of  con- 
trolling, distributing,  and  utilizing  this  energy  as  useful  work. 
Conductors  and  insulating  materials  are  necessary.  Trans- 
mission problems  are  principally  problems  of  high  voltage  and 
therefore  of  dielectrics.  In  order  that  energy  may  flow  along  a 
conductor,  energy  must  be  stored  in  the  space  surrounding  the 
conductor.  This  energy  is  stored  in  two  forms,  electromagnetic 
and  electrostatic.  The  electromagnetic  energy  is  evinced  by  the 
action  of  the  resulting  stresses,  for  instance,  the  repulsion  be- 
tween two  parallel  wires  carrying  current,  the  attraction  of  a 
suspended  piece  of  iron  when  brought  near  the  wires,  or  better 
yet,  if  the  wires  are  brought  up  through  a  plane  of  insulating 
material,  and  this  plane  is  dusted  with  iron  filings,  and  gently 
tapped,  the  filings  will  tend  to  form  in  eccentric  circles  about  the 
conductors.  These  circles  picture  the  magnetic  lines  of  force 
or  magnetic  field  in  both  magnitude  and  direction.  This  field 
only  exists  when  current  is  flowing  in  the  conductors.  If  now 
potential  is  applied  between  the  conductors,  but  with  the  far 
ends  open  circuited,  energy  is  stored  electrostatically.  The 
resulting  forces  in  the  dielectric  are  evinced  by  an  attraction 
between  the  conductors;  a  suspended  piece  of  dielectric  in  the 
neighborhood  is  attracted.  If  the  conductors  are  brought 
through  an  insulating  plane  as  before,  and  this  is  dusted  with  a 
powdered  dielectric,  as  mica  dust,  the  dust  will  tend  to  form  in 
arcs  of  circles  beginning  on  one  conductor  and  ending  on  the 
other  conductor.  See  Fig.  l(a)  and  (6).  The  dielectric  field 
is  thus  made  as  tangible  as  the  magnetic  field.  Fig  l(c)  is  an 
experimental  plot  of  the  magnetic  and  dielectric  fields.  Fig.  l(d) 
is  the  mathematical  plot.  Fig.  l(c)  represents  the  magnetic  and 

1 


2  DIELECTRIC  PHENOMENA 

dielectric  fields  in  the  space  surrounding  two  conductors  which 
are  carrying  energy.  The  power  is  a  function  of  the  product 
of  these  two  fields  and  the  angle  between  them.  In  comparing 
Figs.  l(c)  and  (d)  only  the  general  direction  and  relative  density 
of  the  fields  at  different  points  can  be  considered.  The  actual 
number  of  lines  in  Fig.  l(c)  has  no  definite  meaning.  The 
dielectric  lines  of  force  in  Fig.  1  (d)  are  drawn  so  that  one  twenty- 
fourth  of  the  total  flux  is  included  between  any  two  adjacent  lines. 
Due  to  the  dielectric  fields,  points  in  space  surrounding  the 
conductors  have  definite  potentials.  If  points  of  a  given  poten- 
tial are  connected  together,  a  cylindrical  surface  is  formed  about 
the  conductor;  this  surface  is  called  an  equipotential  surface. 
Thus,  in  Fig.  l(d),  the  circles  represent  equipotential  surfaces. 
As  a  matter  of  fact,  the  intersection  of  an  equipotential  surface 
by  a  plane  at  right  angles  to  a  conductor  coincides  with  a  magnetic 
line  of  force.  The  circles  in  Fig.  l(d),  then,  are  the  plot  of  the 
equipotential  surfaces  and  also  of  the  magnetic  lines  of  force. 
The  equipotential  surfaces  are  drawn  so  that  one-twentieth  of 
the  voltage  is  between  any  two  surfaces.  For  example:  If 
10,000  volts  are  placed  between  the  two  conductors,  one  con- 
ductor is  at  +5000  volts,  the  other  at  -5000  volts.  The  circle 
( oo  radius)  midway  between  is  at  0.  The  potentials  in  space  on 
the  different  equipotential  surfaces,  starting  at  the  positive  sur- 
faces, are  +5000,  +4500,  +4000,  +3500,  +3000,  +2500,  +2000, 
+  1500,  +1000,  +500,0,  -500,  -1000,  -1500,  -2000,  -2500, 
-3000,  -3500,  -4000,  -4500,  -5000.  A  very  thin  insulated 
metal  cylinder  may  be  placed  around  an  equipotential  surface 
without  disturbing  the  field.  If  this  conducting  sheet  is  con- 
nected to  a  source  of  potential  equal  to  the  potential  of  the  surface 
which  it  surrounds,  the  field  is  still  undisturbed.  The  original 
conductor  may  now  be  removed  without  disturbing  the  outer 
field.1 

The  dielectric  lines  of  force  and  the  equipotential  surfaces  are 
at  right  angles  at  the  points  of  intersection.  The  dielectric  lines 
always  leave  the  conductor  surfaces  at  right  angles.  The 
equipotential  circles  have  their  centers  on  the  line  passing  through 
the  conductor  centers,  the  dielectric  force  circles  have  their 
centers  on  the  neutral  line. 

Energy  does  not  flow  unless  these  two  fields  exist  together — 
for  instance,  if  the  dielectric  field  exists  alone  it  is  aptly  spoken 
of  as  "static." 

1  Plots  made  by  the  author  and  first  published  in  the  G.  E.  Review, 
Dec.,  1914. 


<§ 


INTRODUCTION  3 

The  energy  stored  in  the  dielectric  field  is 

^C 
2 

where  e  is  the  voltage  and  C  a  constant  of  the  circuit  called  the 
permittance  (capacity)  and  the  energy  stored  in  the  magnetic 
field  is 


where  i  is  the  current  and  L  is  a  constant  of  the  circuit  called  the 
inductance. 

The  energy  stored  in  the  dielectric  circuit  is  thus  greater  for 
high  voltage,  and  in  the  magnetic  circuit  for  high  currents. 

When  energy  was  first  transmitted,  low  voltages  and  high  cur- 
rents were  used.  The  magnetic  circuit  and  magnetic  field  in  this 
way  became  known  to  engineers,  but  as  little  trouble  was  had 
with  insulation,  the  dielectric  field  was  therefore  not  generally 
considered.  If  insulation  broke  down,  its  thickness  was  in- 
creased without  regard  to  the  dielectric  circuit. 

A  magnetic  circuit  is  not  built  in  which  the  magnetic  lines  are 
overcrowded  in  one  place  and  undercrowded  in  another  place  — 
in  other  words,  badly  out  of  balance.  Since  voltages  have 
become  high  it  is  of  great  importance  to  properly  proportion  the 
dielectric  circuit.  Although  an  unbalanced  magnetic  field  may 
mean  energy  loss,  an  unbalanced  or  too  highly  saturated  dielec- 
tric field  will  mean  broken  down  insulation. 

The  dielectric  and  magnetic  fields  may  be  treated  in  a  very 
similar  way.1  For  instance,  to  establish  a  magnetic  field  a  mag- 
neto-motive force  is  necessary;  to  establish  a  dielectric  field  an 
electro-motive  force  is  necessary.  If  in  a  magnetic  circuit  the 
same  flux  passes  through  varying  cross  sections,  the  magneto- 
motive force  will  not  divide  up  equally  between  equal  lengths  of 
the  circuit.  Where  the  lines  are  crowded  together  the  magneto- 
motive force  per  unit  length  of  magnetic  circuit  will  be  larger  than 
where  the  lines  are  not  crowded  together.  The  magneto-motive 
force  per  unit  length  of  magnetic  circuit  is  called  magnetizing 
force.  Likewise  for  the  dielectric  circuit  where  the  dielectric 
flux  density  is  high  a  greater  part  of  the  electro-motive  force  per 
unit  length  of  circuit  is  required  than  at  parts  where  the  flux 
density  is  low.  Electro-motive  force  or  voltage  per  unit  length 

*See  Karapetoff,  "  The  Magnetic  Circuit,"  and  "  The  Electric  Circuit." 
Steinmetz,  "Electric  Discharges,  Waves  and  Impulses." 


4  DIELECTRIC  PHENOMENA 

of  dielectric  circuit  is  called  electrifying  force,  or  voltage  gradient. 
If  iron  or  material  of  high  permeability  is  placed  in  a  magnetic 
circuit  the  flux  is  increased  for  a  given  magneto-motive  force. 
If  there  is  an  air  gap  in  the  circuit  the  magnetizing  force  is  much 
greater  in  the  air  than  in  the  iron.  If  a  material  of  high  specific 
capacity  or  permittivity,  as  glass,  is  placed  in  the  dielectric  circuit, 
the  dielectric  flux  is  increased.  If  there  is  a  gap  of  low  permit- 
tivity, as  air,  in  the  circuit,  the  gradient  is  much  greater  in  the 
air  than  in  the  glass.  The  electric  circuit  is  also  analogous,  as 
will  appear  later. 

A  given  insulation  breaks  down  at  any  point  when  the  dielec- 
tric flux  density  at  that  point  exceeds  a  given  value.  It  is  thus 
important  to  have  uniform  density.  The  flux,  ^,  depends  upon 
the  voltage,  the  permittivity,  or  specific  capacity  of  the  insulation, 
and  the  spacing  and  shape  of  the  terminal.  That  is, 

j,  =  Ce 

The  flux  density  Z>,  at  any  point,  is  proportional  to  the  gradient 
g,  or  volts  per  centimeter  at  that  point,  and  to  the  permittivity  of 
the  dielectric.  Thus, 

D  =  ^  Kk  =  gKk 
ax 

also  D  =  -r 

As  the  density  is  proportional  to  the  gradient,  insulations  will, 
therefore,  also  rupture  when  the  gradient  exceeds  a  given  value; 
hence  if  the  gradient  is  measured  at  the  point  of  rupture  it  is  a 
measure  of  the  strength  of  the  insulation.  The  strength  of  in- 
sulation is  generally  expressed  in  terms  of  the  gradient  rather  than 
flux  density. 

By  analogy  with  Hooke's  Law  the  gradient  may  be  thought 
of  as  a  force  or  stress,  and  the  flux  density  as  a  resulting  electrical 
strain  or  displacement.  Permittivity,  k,  then,  is  a  measure  of 
the  electrical  elasticity  of  the  material.  Energy  is  stored  in  the 
dielectric  with  increasing  force  or  voltage  and  given  back  with 
decreasing  voltage.  Rupture  occurs  when  the  unit  force  or 
gradient  exceeds  the  elastic  limit.  Of  course,  this  must  not  be 
thought  of  as  a  mechanical  displacement.  In  fact,  the  actual 
mechanism  of  displacement  is  not  known. 

When  two  insulators  of  different  permittivities  are  placed  in 
series  with  the  same  flux  passing  through  them,  the  one  with  the 


INTRODUCTION  5 

lower  permittivity  or  less  electrical  elasticity  must  take  up  most 
of  the  voltage,  that  is,  the  " elastic"  one  may  be  thought  of  as 
"stretching"  electrically  and  putting  the  stress  on  the  electrically 
stiff  one.  The  dielectric  circuit  is  also  analogous  to  the  electric 
circuit  when  the  flux  is  thought  of  in  place  of  the  current — and 
the  permittance  as  conductance.  The  reciprocal  of  the  permit- 
tance is  sometimes  called  the  elastance  (S)  and  corresponds  to 
" resistance"  to  the  dielectric  flux.  It  is  convenient  when 
permittances  are  connected  in  series,  as  the  total  elastance  is  the 
sum  of  the  elastances.  When  permittances  are  connected  in 
multiple,  the  total  permittance  is  the  direct  sum  of  the  permit- 
tances. Take  two  metal  plates  in  air  and  apply  potential 
between  them  until  the  flux  density  is  almost  sufficient  to  cause 
rupture.  Now  place  a  thick  sheet  of  glass  between  the  plates; 
the  permittance  and  therefore  the  total  flux  is  increased.  This 
increases  the  stress  on  the  air,  wliich  breaks  down  or  glows. 
The  glass  does  not  break  down.  Thus  by.  the  addition  bf  insu- 
lation the  air  has  actually  been  broken-  down.  This  takes  place 
daily  in  practice  in  bushing,  etc.,  and  the  glow  is  called  static. 

It  is  especially  important  in  designing  leads  and  insulators  im- 
mersed in  air  to  avoid  overstress  on  the  ahv 

It  can  be  seen  that  a  statement  of  volts  and  thickness  does  not 
determine  the  stress  on  the  insulation.  'The  stress  on  insulation 
does  not  depend  altogether  upon  the.  voltage,  but  also  upon  the 
shape  of  the  electrodes;  as,  for  instance,  for  needle  points  the  flux 
density  at  the  point  must  be  very  great  at  fairly  low  voltages, 
while  for  large  spheres  a  very  high  voltage  is  required  to  pro- 
duce high  flux  density.  For  this  reason  200  kv.  will  strike  55 
cm.  between  needle  points,  while  it  will  strike  only  about 
17  cm.  between  12.5-cm.  spheres.  From  the  above  it  can  be 
seen  that  it  is  much  more  important  to  design  the  dielectric 
circuit  for  proper  flux  distribution  than  the  magnetic  circuit. 
Local  overflux  density  in  the  magnetic  circuit  may  cause  losses, 
but  local  overflux  density  in  the  dielectric  circuit  may  cause 
rupture  of  the  insulation. 

Consider  now  the  two  conductors  of  a  transmission  line  with 
voltage  between  them.  The  total  dielectric  flux  begins  on  one 
conductor  and  ends  on  the  other  conductor  (see  Fig.  l(d)).  The 
flux  is  dense  at  the  conductor  surface  and  less  so  at  a  distance 
from  the  conductor.  Hence  the  voltage  gradient  is  greatest 
at  the  surface,  where  the  dielectric  cross-section  is  a  minimum, 


6 


DIELECTRIC  PHENOMENA 


and  therefore  the  "flux  resistance"  or  elastance  is  greatest  and 
breakdown  must  first  occur  there.  For  the  particular  case  shown 
in  Fig.  2  one-third  of  the  voltage  is  taken  up  by  the  space  12  cm. 
from  each  conductor,  although  the  total  space  is  100  cm.  The 
gradient  is  greatest  at  the  wire  surface.  That  is,  if  across  a 
small  distance,  Xi,  the  voltage  is  measured  near  the  wire  surface 
and  then  again  across  the  same  space  X2  some  distance  from  the 
wire,  it  is  found  that  the  voltage  is  much  higher  across  the  small 

space  Xi  near  the  wire 


JTl-»lj-l  Cm 


+50- 


l^K.V. 


M.6  K. 


klCm 


lCm-» 


-50 


surface  than  across  the 
one  farther  out.  In  ac- 
tually measuring  the 
gradient,  or  rather  cal- 
culating it,  X  is  taken 
very  small  or  dx.  The 
voltage  across  dx  is  de. 
The  purely  mathemat- 
ical expression  for  the 
gradient  at  the  surface 
of  parallel  wires  is: 


dx 


2r 


FIG.  2. — Voltage  in  space  between  two  par- 
allel wires. 


If  the  conductors  are 
close  together  a  spark 
jumps  across  when  the 
voltage  is  high  enough  to 

produce  overflux  density  at  the  conductor  surface;  or  corona  and 
spark-over  are  simultaneous.  If  far  apart,  corona  forms  around 
the  conductor  surface  and  sparkover  takes  place  at  some  higher 
voltage. 

As  voltages  or  electro-motive  forces  become  higher  the  proper 
shaping  and  spacing  of  the  conductors  to  prevent  dielectric  flux 
concentration  becomes  of  more  importance.  The  dielectric 
field  must  now  be  considered  in  the  design  of  apparatus  as  the 
magnetic  field  has  been  considered.  Certain  phenomena  always 
exist  which  go  unnoticed  because  of  their  feeble  effect,  but  which 
when  conditions  are  changed,  usually  in  a  way  to  cause  a  greater 
energy  density,  become  the  controlling  features.  This  is  so  with 
the  dielectric  circuit.  The  problem  first  made  itself  apparent  to 


INTRODUCTION  1 

engineers  in  the  transmission  line,  which  will  be  taken  to  illus- 
trate this.  When  voltages  were  below  about  60,000  the  conduc- 
tors used  had  sufficient  radius  or  circumference  so  that  the  surface 
flux  density  or  gradient  was  not  sufficient  to  cause  breakdown. 
As  voltages  became  higher  the  sizes  of  conductors  remained 
about  the  same,  and  therefore  the  flux  density  or  gradient  became 
greater.  The  air  broke  down  and  caused  the  so-called  corona 
and  resulting  loss. 

As  high  voltage  engineering  problems  will  be,  to  a  great  extent, 
problems  of  the  dielectric  circuit,  this  will  be  discussed  iii  the  next 
chapter  and  calculations  made  for  a  few  common  forms  of  elec- 
trodes. The  determination  of  the  dielectric  flux  density,  etc., 
is  purely  a  mathematical  problem.  Exact  calculations  are  diffi- 
cult and  often  impossible  except  for  simple  forms.  Exact  calcu- 
lations are  not  necessary  in  practical  design  work,  but  the  general 
principles  must  be  kept  in  mind. 


CHAPTER  II 
THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT 

If  two  conductors  placed  in  a  dielectric,  as,  for  instance,  the 
two  parallel  wires  of  a  transmission  line  in  air,  are  connected 
together  at  one  end  by  an  electric  motor,  or  resistance  and  poten- 
tial is  applied  across  the  other  end  from  an  a.c.  generator  or 
other  source  of  power  supply  (see  Fig.  3),  energy  transfers  take 
place.  The  motor  at  the  far  end  turns  and  part  of  the  energy  is 
thus  used  as  useful  work — part  appears  as  heat  in  the  motor. 


TT  TTTT 


FIG.  3. — Transmission  line  carrying  energy. 

As  a  function  of  the  current  in  the  transmission  circuit  and  a 
constant  called  the  resistance,  energy  is  absorbed.  This  energy 
appears  as  heat  in  the  conductors ;  it  is  proportional  to  the  product 
of  the  square  of  the  current  and  the  resistance,  and  is  commonly 
known  as  the  I2r  loss.  Hence,  as  it  is  not  returned  to  the  circuit 
or  transferred  into  useful  work,  but  is  dissipated  as  heat,  it  is 
analogous  to  a  friction  loss.  During  the  transmission,  energy 
is  stored  in  the  space  surrounding  the  conductors  in  the  electric 
field  in  two  different  forms — magnetic  and  dielectric. 

Energy  is  stored  in  the  magnetic  field,  where  it  is  proportional 

8 


THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT       9 

to  the  square  of  the  current  and  to  a  constant  of  the  circuit  called 
the  inductance: 

PL 


Magnetic  energy  is  stored  with  increasing  current  and  delivered 
back  to  the  circuit  with  decreasing  current.  The  magnetic 
energy  becomes  noticeable  or  large  when  the  currents  are  large, 
or  in  low  voltage  circuits. 

Due  to  the  dielectric  field,  the  energy  is 


\AAA7 


Wc   = 


This  energy  is  stored  with  increasing  voltage  and  delivered  back 
with  decreasing  voltage.  A  dielectric  may  thus  by  analogy  be 
thought  of  as  an  electrically 
elastic  material,  which  is  dis- 
placed by  an  electric  pressure, 
i.e.,  voltage.  Energy  is  hence 
stored  in  the  dielectric  with  in- 
creasing voltage  or  electric 
pressure,  is  maximum  at  the 
maximum  point  of  the  voltage 
wave  and  is  delivered  back  to 
the  circuit  with  decreasing 
voltage.  When  the  pressure 
becomes  too  great  the  electric 
11  elastic  limit"  is  exceeded,  or 
the  dielectric  becomes  dis- 
torted beyond  this  "elastic 
limit,"  and  rupture  occurs. 

The  dielectric  energy  becomes        FlG-  4.— Variation  of  dielectric  and 
.  .  magnetic  stored  energy  with  voltage 

of   great  importance   at  high     and  current. 

voltage,  and  hence  in  the  study 

of  insulations,  and  it  only  will  be  considered  here.  The  electric 
displacement  may  be  pictured  in  magnitude  and  direction  by 
lines  of  force.  The  dielectric  lines  of  force  for  two  parallel  con- 
ductors are  shown  in  Fig.  3,  the  eccentric  circles  (dotted)  are  the 
magnetic  lines  of  force.  The  magnetic  circles  are  also  equipo- 
tential  boundary  lines  for  the  dielectric  field.  The  dielectric 
energy  is  sometimes  said  to  be  due  to  a  charge  on  the  con- 
ductor, This  is  often  confusing,  as  the  energy  is  stored  not 


540  < 


720< 


Time 


10 


DIELECTRIC  PHENOMENA 


on  the  conductor  but  in  the  surrounding  space,  and  may  be 
thought  of  as  due  to  an  electric  displacement.  The  nature 
of  this  displacement  is  not  known.  It  can  be  seen  that  in 
order  that  a  transfer  of  energy  may  take  place,  energy  must  be 
stored  in  the  space  surrounding  the  conductors  in  two  forms — 
magnetic  and  dielectric.  Energy  thus  flows  only  in  a  space  in 
which  there  is  a  magnetic  and  a  dielectric  field.  This  energy 
is  proportional  to  the  product  of  the  magnetic  and  dielectric 
field  intensity  and  the  sine  of  the  included  angle.  If  one  field 
exists  alone  there  can  be  no  energy  flow.  The  change  of  stored 
energy  from  magnetic  to  dielectric  and  back  is  shown  in  Fig.  4. 
Dielectric  Field  between  Parallel  Planes. — In  the  dielectric 
field  the  flux  or  total  displacement  is 

\f/  =  Ce  coulombs  (or  lines  of  force)  (1) 

where  e  is  the  applied  e.m.f.  or  voltage,  and  C  is  a  constant  of  the 
circuit,  depending  upon  its  dimensions,  and  is  called  the  capacity, 


FIG.  5. — Dielectric  field  between  parallel  planes. 

or  better,  permittance.  If  C  is  measured  in  farads,  and  e  in  volts, 
\l/  is  expressed  in  coulombs.  Fig.  5  shows  the  simplest  form  of 
dielectric  circuit.  Neglecting  the  extra  displacement  at  the  edges, 
it  is  seen  that  the  dielectric  lines  of  force  are  everywhere  parallel 
and  the  field  is  uniform.  The  dielectric  circuit  constant,  or  the 
permittance,  is  directly  proportional  to  the  area  of  the  cross- 
section  perpendicular  to  the  lines  of  force,  inversely  propor- 
tional to  the  spacing  along  the  lines  of  force,  and  directly  propor- 
tional to  the  dielectric  constant  or  the  permittivity. 

For  large  parallel  planes  without  flux  concentration  at  the  edges 


(2) 


THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT       11 

where   A  is  the  area  in  square  centimeters, 

X  is  the  distance  between  plates  in  centimeters, 

k  is  the  specific  inductive  capacity,  or  better,  permittivity, 

and 
v    is  the  velocity  of  light,  3  X  1010  cm.,  per  second. 

The  term  in  brackets  is  due  to  units.     The  flux  density  then, 
or  displacement  per  unit  area,  as  the  flux  is  uniform,  is: 

t        Ce       e/clO9 

1  =:  ~A    =          *  coulombs  per  cm.2 


To  establish  this  flux  or  displacement  through  the  distance  X  an 
electromotive  force  e  is  required.  The  force  per  unit  length  of 
dielectric  circuit  or  electrifying  force  is  constant  in  the  uniform 

o 

field  and  is  then  ^.     The  gradient  then  is 
JL 

p 

g  =  -^  volts/cm. 
y\. 

The  density  may  thus  be  written: 


which  is  analogous  to  Hooke's  law  in  Mechanics, 
strain  =  k  times  stress. 

The  larger  k  is,  the  greater  the  displacement  is  for  a  given 
force  g. 

Thus  k  is  the  coefficient  indicating  electrical  elasticity  of  the 
material,  or  its  "  conductivity"  to  the  flux.  The  reciprocal  of 
permittivity  is  analogous  to  resistivity  and  has  been  termed 
elastivity  (<r).  The  reciprocal  of  permittance  has  been  termed 
elastance  (S)  .  The  dielectric  circuit  then  becomes  analagous  to 
the  electric  circuit 

volts  e 

Flux  =  775—     —  -r—     —77  or  ^  =  -~ 

flux  resistance"  S 

It  is  often  convenient  to  consider  the  dielectric  circuit  in  this 
way,  and  to  use  cr  and  S,  as  the  total  elastance  of  a  number  in 
series  is  the  direct  sum.  The  total  permittance  of  a  number  in 
multiple  is  the  direct  sum.  See  two  methods,  Case  1,  Chapter  X. 


12  DIELECTRIC  PHENOMENA 

In  studying  insulations  it  is  important  to  be  able  to  express 
their  relative  strengths.  This  is  naturally  generally  done  in 
terms  of  the  force  or  voltage  gradient  necessary  to  cause  rupture. 
It  may  also  be  done  in  terms  of  the  flux  density  at  rupture;  that 
is,  in  coulombs  per  square  centimeter.  A  given  insulation  breaks 
down  at  any  point  when  the  flux  density  exceeds  a  certain  defi- 
nite value  at  that  point,  or  when  the  gradient  exceeds  a  given 
definite  value. 

For  Fig.  5  where  the  field  is  uniform  the  gradient  is 


109 
K  =  -.—»  =  8.84  X  10~14 


Hence,  if  the  voltage  is  increased  until  rupture  occurs,  and  found 
to  be  et  the  voltage  gradient  or  the  flux  density  at  rupture  is 
known;  it  would  seem  that  this  would  be  a  good  form  of  test 
piece  with  which  to  study  insulation.  This  is  not  usually  the 
case  because  of  the  extra  displacement  at  the  edges  which  is  dif- 
ficult to  calculate.  This  may,  however,  be  made  very  small  at 
small  spacings  by  proper  rounding  of  the  edges.  Equations  for 
the  voltage  gradient,  permittance,  etc.,  will  now  be  given  for  a 
few  of  the  common  electrodes.  In  general,  calculations  are  made 
in  the  same  way,  except  that  the  field  is  usually  uniform  over  only 
very  small  distances.  The  total  capacity  is  found  by  taking  the 
capacities  over  distances  so  small  that  conditions  are  still  uniform 
and  integrating. 

Concentric  Cylinders.  —  Concentric  cylinders  make  a  conven- 
ient arrangement  for  studying  dielectric  strength,  especially  that 
of  air  and  oil.  On  account  of  the  symmetrical  arrangement,  the 
dielectric  circuit  is  readily  calculated.  For  testing,  the  extra 
displacement  at  the  ends  is  eliminated  by  belling  (see  Fig.  6). 

Permittance  or  Capacity.  —  In  this  case  the  lines  of  force  are 
radial.  The  equipotential  surfaces  are  concentric  cylinders. 
The  total  flux  per  centimeter  length  of  cylinder  is 

t  =  Ce 

The  permittance  may  be  thought  of  as  made  up  of  a  number  of 
permittances  in  series  between  r  and  R,  each  permittance  being 
between  two  equipotential  surfaces  dx  centimeters  apart. 


THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT      13 
For  a  number  of  permittances  in  series 

--—+—  +  . 

C        Ci        Cz 


Lines  of          X^  > 

Force 

FIG.  6. — Concentric  cylinders. 

The  permittance  of  the  condenser  of  thickness  dx,  over  which  the 
field  is  uniform  (Fig.  6),  per  centimeter  length  of  cylinder  is 

dx  4irv2         2v2   dx 


aHiUig).**g;.g 


f*x  =  R  f*x  -  R  f*x  = 

i=S=    I  d©=    I  dS  =  j£j5  I  f 
I      \C/        I  fclO     I    x 

t/a;  =  r  t/a:  =  r  »y  x  =  r 


/blO9      MO9  x 

-B 


C  =         fcl°9  5.55  HO-13      farads  per  centimeter 

2vz  loge  R/r  =       loge  R/r        length  of  cylinder. 

Gradient  and  Flux  Density. — The  flux  density  is  greatest  at  the 
conductor  surface  and,  hence,  the  gradient  must  be  greatest 
there.  The  flux  density  at  any  point  x  measured  from  the  center 
is 


A       A       A2v*  loge  R/r 
A  =  2irx 

n ^_-_  1Q9  =  0.884  -  T*—  ID-"   coulombs 

loge  R/r  x  loge  R/r  per  cm.2 


-  P 

D      -  10-9  =  —r—trr  kv.  per  cm.  (6) 

k  x  loge  #/r 

g  is  maximum  at  the  surface  of  the  inner  cylinder  or 
where  x  =  r 


14 


DIELECTRIC  PHENOMENA 


Parallel  Wires. — Parallel  wires,  one  of  the  most  common  prac- 
tical cases,  will  be  considered  in  detail,  in  order  to  illustrate  the 
general  method  of  calculating  the  dielectric  circuit  and  to  show 
that  the  expressions  for  the  permittance,  flux  density,  gradient, 
etc.,  are  quite  simple  and  can  be  written  with  the  aid  of  ordinary 
geometry  and  calculus. 

Equipotential  Surfaces,  Lines  of  Force,  and  Flux  Density. — All 
of  the  equipotential  surfaces  which  arise  in  this  case  are  cylin- 
drical. Therefore,  only  their  intersections  with  a  normal  plane 
need  be  considered,  and  the  problem  may  be  dealt  with  as 
affecting  only  the  plane. 


Fix.  7. — Lines  of  force  between  parallel  wires,  by  superposition  of  inde- 
pendent radial  fields. 

The  following  principles  will  be  used: 

(1)  The  resultant  field  in  the  space  between  two  conductors 
is  the  superposition  of  the  two  independent   fields.     The  re- 
sultant field  due  to  any  number  of  fields  may  be  found  by 
combining  in  pairs. 

Fluxes  may  be  added  directly. 

(2)  The  potential  at  any  point  is  the  algebraic  sum  of  the 
potentials  due  to  the  independent  fields  through  that  point. 
In  the  same  way,  the  potential  difference  between  two  points 


THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT       15 


FIG.  8 (a). — Lines  of  force  and  equipotential  surfaces  between  parallel  wires. 


FIG.  8(b). — Lines  of  force,  equipotential  surfaces,  and  equigradient  surfaces 
between  parallel  wires. 


16  DIELECTRIC  PHENOMENA 

is  the  algebraic  sum  of  the  potential  differences  due  to  the 
independent  fields. 

(3)  The  density  or  gradient  at  a  point  is  the  vector  sum  of 
the  densities  or  gradients  due  to  the  independent  fields. 

When  the  conductors  are  infinitely  small,  the  dielectric  field 
may  be  considered  as  that  resulting  from  the  superposition  of 
the  two  uniform  radial1  fields  from  the  conductors  to  an  infinite 
cylinder. 

The  resultant  equipotential  surfaces  are  then  cylinders  whose 
right  sections  are  eccentric  circles  which  enclose  the  wires,  and 
whose  centers  all  lie  in  the  line  connecting  them ;  and  the  lines  of 
force  are  arcs  of  circles  intersecting  in  the  conductors.  The 
independent  radial  fields  about  each  conductor  are  shown  in  Fig. 
7,  and  the  field  resulting  by  superposition  is  shown  in  Fig.  8. 


FIG.  9. 

The  equipotential  surfaces  will  first  be  considered.  It  has  been 
shown  above  that  the  permittance  C  between  two  equipotential 
cylinders  of  radii  R  and  r  is 

C  =  ,  -  ^rr  farads  per  cm.  (5) 

R/r 


This  is  also  the  permittance  between  any  two  points  on  these 
surfaces;  therefore,  the  voltage  between  points  distant  TI  and  rz 
cm.  from  the  conductor  center  is 


erir2  = 


Considering    now   the   field    resulting  from   superposition:     In 

1  By  uniform  radial  field  is  meant  one  in  which  equal  central  angles  always 
include  equal  fluxes. 


THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT      17 

Fig.  9,  the  potential  difference  between  H2  and  P,  due  to  the 
radial  flux  ^  from  A\,  is 


Similarly,  the  potential  difference  between  H  2  and  P,  due  to  the 
radial  flux  —  ^  from  A'  2,  is1 

-  I  loge  a?2/  & 


The  total  potential  difference  between  #2  and  P  due  to  the  two 
radial  fields,  and  hence  due  to  the  resultant  field,  is  the  algebraic 
sum  of  the  potential  difference  produced  by  each  field  separately  : 


But  if  Hz  and  P  are  points  on  the  same  equipotential  surface 
the  potential  difference  between  them  is  zero,  or 


Therefore  log*-1  =  logc|-2 

a  o 

Xi          Xz 

a  "  b 

Xi       a 

-  =  T  =  const. 
xz       o 

if  HI  is  fixed  —  that  is,  for  any  one  equipotential  surface. 

The  equipotential  surfaces  are  cylinders  whose  sections  are 
circles  which  surround  the  infinitely  small  conductors.  These 
circles  have  centers  on  line  AiA2,  but  are  not  concentric  with  the 
conductors.  This  may  be  shown  as  follows: 

Assume  Cartesian  axes  through  A'2,  the  X  axis  containing  Ar\. 
Let  the  coordinates  of  P  be  x,  y, 

xl  =  V(A'lAfz  -  xY  +  y2  =  V(a  +  b-x)*  +  y* 
xz  =  \/x2  +  y2 


Xi  _  a         l(a 
X,  ~  b  ~  V" 


+  b  -  x) 


1  The  signs  must  always  be  properly  placed.  It  is  convenient  to  give  \f/ 
the  sign  of  the  point  displacement  under  consideration.  The  distances  from 
the  displacement  points  to  the  points  between  which  potential  is  sought 
should  always  be  put  in  the  same  order  in  the  log,  as,  Xi/a,  xz/b,  etc.  See 
problems,  Case  11  and  Case  12,  Chap.  X. 
2 


18 


DIELECTRIC  PHENOMENA 


(a2- 

X2     I 


a2  +  b4  +  b2x2  +  2ab3  -  2ab*x  -  2b*x 
262(a  +  b)x  +  (a2  - 


x  + 


tt-b      '    (a-  b) 

62 


a2  -  62      '    (a  -  6) 


, 
r 


a  - 


i       ,= 


(a  -  6)2  (a-4  &)2 


(7) 


This  is  the  equation  of  a  circle  whose  center  has  the  coordinates 

•9     ft  7 

0  and  whose  radius  is  —  :— r-    The  circle  is  thus  found  for 


a-  b 


a-b 

any  given  a  and  6. 

The  equipotential  circle  through  any  point  P  (xp,  yp)  is  found 
as  follows: 


a  = 


b  = 


a  +  6  Xi  +  z2 

Substituting  for  a  and  6  in  (7) : 


*  + 


flT^£f) 

+  W 


>S/2 


(« 


4-  2/2  = 


a:22  =  a;p2  4-  2/p2 

/ x  +  (jcrL±yr        ,  , 

V  x        S'2  ' 


-*S/2 


resultant  lines  of  force  are  arcs  of  circles  with  centers  on 
line  n  and  passing  through  the  points  A'i  and  A'2.  This  is  shown 
as  follows:  Consider  Fig.  10.  The  flux  included  in  PA'i  A'2  per 


THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT       19 


centimeter  length  of  cylinder  due  to  A\  is  -.     That  in  PA'Z 


A'  i  due  to  A'2  is  -^—  . 

ZTT 

The  total  flux  between  P  and  A'i  A'z  is  the  sum  of  these, 

$p   =  FT  («i  +  "2) 

The  restriction  that  lines  of  force  cannot  cross  implies  that  the 
flux  between  any  two  is  constant;  hence  if  P  move  along  a  flux 
line, 


=  const' 


from  which 


~\~  <*2  =  const. 


Hence: 

a  =  TT  —  (ai  +  0:2) 


const. 


NOTE. — The  equation  of  the 
line  of  force  may  also  be  found 
by  writing  the  expression  for  FIG.  10. 

the  flux  densities  at  points  and 
imposing  the  condition  that  the  component  normal  to  the  line  of  force  is  zero. 

This  condition  defines  a  circular  arc  passing  through  A\  and 
A'z.  Choosing  as  before  the  point  A' 2  as  the  origin  of  Cartesian 
coordinates,  the  equation  of  these  circles  is: 


(f  - 


(y  - 


(8) 


where  m  is  the  ordinate  of  the  center  of  any  particular  circle. 
The  equation  of  the  line  of  force  through  (x,  y)  is  found  as 
follows  : 

Call  the  center  of  circle  (lines  of  force)  0 
A2'0  =  PO  =  radius  of  circle 


(8) 


Through  any  point  (xpyp). 


20  DIELECTRIC  PHENOMENA 

Then  (^  -  a*) 2  +  (yP  -  m)2  =  (|')  + 

+  i/P2  -  S'ZP 


Substituting  this  value  of  m  in  (8)  : 


,    /S 
\2/ 


2yp 

The  slope  of  the  equipotential  surface  at  (xp,  yp)  is  found 
from  (la). 

Evaluate  y  in  terms  of  x,  differentiate,  and  put  x  —  xp. 

NOTE. — Take  x  always  +•     m—  when  below  x  axis. 

dy  S'XP  —  XPZ  H-  yp2 

dxea  ~  yP(S'  -  2xP) 

The  slope  of  the  line  of  force  at  (xp,  yP)  is  found  in  the  same  way 
from  (8a) 

dy  yP(S'  -  2xP) 

dxif       r  S'XP  -  xP2  +  yP2 

It  will  at  once  be  noticed  that 

dy 


dxes  ~  dx 

which  shows  that  the  line  of  force  at  any  point  is  perpendicular  to 
the  equipotential  surface  at  the  same  point. 

The  flux  density,  D,  at  any  point  in  the  resultant  field  is  the 
vector  sum  of  the  flux  densities  due  to  A' \  and  A'2  separately.  At 
P  (Fig.  10)  the  flux  density  due  to  A'i  is 


and  due  to  A'z  is 


directed  as  indicated. 

NOTE.  —  Subscript  es  refers  to  equipotential  surface. 
Subscript  If  refers  to  line  of  force. 


THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT      21 


The  triangles  whose  sides  are  x\,  x%,  S'  and  DZ)  DI,  D  may  be 
shown  to  be  similar,  having  one  angle  (a)  equal,  and  the  including 
sides  proportional. 

* 


Then 


D 

S' 


D  = 


(9) 


The  preceding,  covering  infinitely  small  wires,  is  not  directly 
applicable  to  the  ordinary  case  of  large  parallel  wires.  Green's 
theorem,  however,  states  that  if  any  equipotential  surface  be 
kept  at  its  original  potential,  the  flux  within  it  may  be  removed 
without  any  change  in  the  external  field.  In  Fig.  11  the  circle* 


FIG.  11. 

represent  equipotential  cylinders,  surrounding  flux  centers  A'i 
and  A  '2.  These  cylinders  may  be  maintained  at  their  original 
potential.  The  interior  may  be  filled  with  a  conductor.  This 
gives  parallel  conductors  of  radius  r  and  spacing  between  centers 
S.  The  external  field  has  not  been  changed,  and  the  preceding 
discussion  still  applies.  A\  and  A%  must  be  located  from  A\ 
and  A  '2,  since  r  and  S  are  the  quantities  given  in  any  actual  case. 
This  is  easily  done  : 

S  —  r  —  z 


a 
b 

z  = 
zS  = 

»2     . 


Z    = 


r  —  z 


r2  -  2rz 


a  -  b       S  -  r 

Sz  +  r2  =  0 
S  -      ' 


z  —  r 


r2  -  2rz  + 
S  -  2r 


-  4r2 


22  DIELECTRIC  PHENOMENA 

Since  obviously  z  cannot  be  greater  than  $/2,  the  negative  sign 
is  taken  for  the  radical. 

a  =  S  —  r  —  z 
2S  ~  2r  ~  S 


~  2r 


2 
b  =  r-z 


2r  -  S  +   V$2-  4r2 


a       S  -  2r  +        2  -  4r2 


2r  -  S  +         2  -  4r2 


>S  -  2r  +   ViS2  -  4r"2       2r  -  £  -• 


2r  -  S  +   V£2  -  4r2       2r  -  S  - 

-  2r)  VS2  -  4T2 


2r(2r  -  5) 


Permittance  or  Capacity.  —  In  Fig.  11  let  n  be  a  neutral  plane. 
Represent  by  en  the  potential  between  circle  H2  and  n  (or  //i 
and  n)  and  by  Cn  the  corresponding  permittance  to  neutral  per 
centimeter  length  of  wires.  Due  to  A'\. 


6nl~        2<jrkK 
Due  to  A'  z. 


\/  i 

en  =  enl  +  enZ=  ioge          "  loge 


2irkK 
a 


THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT      23 

Substituting  from  (10) 

_  2irkK 

=  (11) 

2-irkK 


5.55MO-13  ,       , 

farads  per  cm. 


If  hyperbolic  tables  are  available,  a  more  convenient  form  is 
2irkK 


Cn  = 


.8  (lie) 

"1  — 


, 
cosh 


5.55/clO-13 

—  ~—  farads  per  cm. 

cosh-1  — 


If  S/r  be  large,  then  ,*/(  —  )     —  1  is  nearly  equal  to  nT1 
approximately 

Cn  =  -j —    0  /    farads  per  cm.  (H&) 

The  result  corresponds  exactly  to  the  form  (page  22)  which 
would  have  resulted  had  the  wires  been  considered  very  small  at 
the  start,  or 

2wkK 

n       loge  a/b 
where       a  =  S,  b  =  r 

Gradient  and  Flux  Density. — The  flux  density  at  any  point  on 
the  line  joining  the  centers  of  the  conductors  and  distant  x  from 
the  inner  surface  of  one  of  them  is 


2irXiX2  Xi  =  a  —  x 

(a  H-  b)\l/ 

2ir(ab  +  (a  -  6)x  -  x2) 


24 


DIELECTRIC  PHENOMENA 


-  4r2 


Since 


=  Cne 


x)  (S  -2r)  - 
2irkKen 


D  = 


-  2r)- 


6*  V©-'] 


(r  +  x)  (S  -  2r)  -  x2)  log,         +       ()2    -  l] 


-  4rHO-13 


|  (r+x)  (S  -  2r)  -  X2! 


The  gradient  along  the  line  of  centers  is 
D 


9  = 


kK 


-  4r2 


coulombs 
per  cm.2 


(12) 
kv.  per 


{(r  +  x)  (S-2r)  -  x* 
The  gradient  is  greatest  at  the  conductor  surface  (x  =  0)  and  is 


cm. 


Qmax    =   —' 


-  4r2 


r(o  — 


(12o) 


^r-kv.  per  cm. 


=~kv.  per  cm. 


Where  hyperbolic  tables  are  available  a  more  convenient  form  is : 


Qmax 


en 


—  kv.  per  cm. 


(126) 


-- 


cosh"1  s- 


THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT      25 

If  S/r  is  large  gmax  =  r  ^  s/r  (12c) 

As  before,  this  equation  would  have  resulted  had  the  conductors 
been  considered  small  in  the  first  place.  The  method  of  drawing 
the  lines  of  force,  etc.,  is  illustrated  in  Chapter  X. 

Spheres. — In  studying  insulation  it  is  sometimes  convenient 
to  use  spherical  electrodes.  The  potential  between  concentric 
spheres  of  radii  R  and  r  may  be  found  as  for  concentric  cylinders 
on  page  13.  The  equipotential  surfaces  are  spheres.  Between 
two  surf  aces  at  distance  x,  dx  centimeters  apart  the  permittance  is : 

,„        ,/l\       dx     I  1      dx 

ao  =  a  (  7^)  =  —r-  j-f=  —  — 

A   kK     47rkK  x2 

_      *     I"*       11 
C      4-jrkKJ  x2       4TrkKlr       Rl 

Rr 


C  = 


-    . 
~       ~ 


R  -  r 

R  ~  r 


C  ~  4irkK      Rr 

The  potential  difference  due  to  \f/  between  two  points  distant 
r\  and  r2  from  the  center  of  the  sphere  is 

*      rJL  JZJJ 
r>r*       4irkK      nr2 

The  equipotential  surfaces  between  two  point  electrodes  or 
very  small  equal  spheres  may  be  found  as  follows,  using  Fig.  11  : 
The  difference  of  potential  between  Hz  and  P  due  to  A'\  is 


a\ 

/ 


due  to  A\  is  ^  = 


-  a      Xz  -  b 

ep  " 


If  H 2  and  P  are  on  the  same  equipotential  surface 
Xi  —  a  _  xz  —  b  _  _ 

ab 

=  constant 


Xz  —  Xi      b  —  a 

; =  constant 

is  the  equation  for  the  equipotential  surface 


26  DIELECTRIC  PHENOMENA 

The  fraction  of  the  total  flux  toward  P  through  the  cone  with 
apex  at  A'i  and  half  angle  a  due  to  A'  is1 

1^1  =  2  (1  -  c°s  «0 

Through  the  cone  with  apex  on  A'2  and  half  angle  az  due  to  A'2, 
it  is 

^ 
=       1  —  cos  *t 


If  P  follows  a  line  of  force  \f/P  must  be  constant  because  lines  of 
force  cannot  cross. 

.*.  cos  ai  +  cos  a  2  =  constant 

is  the  equation  of  the  line  force. 

The  equations  for  the  gradients,  etc.,  of  two  large  spheres  of 
equal  radii  and  spaced  apart  are  given  below: 
Spheres  of  Equal  Size  in  Air  (Non-grounded)  :2 

p 

g  =  —  f  kv.  per  cm.  (13a) 

^L 

where 

g    =  gradient  at  surface  of  sphere  in  line  joining  centers. 
e    =  volts  between  spheres. 

X  =  distance  between  nearest  surfaces  in  centimeters. 
/   =  a  function    of    X/R   where   R   is   the   radius   of 
either  sphere. 

Spheres  of  Equal  Size  in  Air  (One  Sphere  Grounded)  : 
g  =  ^/i  kv.  per  cm. 
g  =  -g  /o  kv.  per  cm.  (136) 

where  the  letters  have  the  meaning  noted  above,  /i  being  a  differ- 
ent function  of  X/R.  For  the  case  of  one  sphere  grounded,  the 
shanks,  connecting  leads,  ground,  etc.,  have  a  much  greater  effect 
than  when  both  are  non-grounded.  For  this  reason  the  theo- 
retical values  of  fi  do  not  check  closely  the  experimental  results 

1  The  area  of  a  spherical  surface  is  4irR2.    The  area  of  a  spherical  sector 
with  half  angle  a  is  2irR*(l  —  cos  a). 
*Russel,  Phil.  Mag.,  Vol.  XI,  1906. 


THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT      27 


and  must  not  be  used.     Experimental  values  for  the  grounded 
case  are  given  as  /o  in  the  accompanying  table. 
/  and /i  may  be  calculated  by  the  following  simple  formulae:1 

X/R  +  1  +  V  (X/R  +  I)2  +  8 


/i  =  V2 


X/R 


(Not  to  be  used 
in  practice) 


x/# 

Calculated 

Measured2 

/ 
Non-grounded 

/i 

Grounded 
(Not  for  use) 

/o 
Grounded 

0.1 

1.034 

1.050 

1.03 

.0.5 
1.0 

1.177 
1.366 

1.282 
1.517 

1.18 
1.41 

2.0 

1.781 

2.339 

1.97 

3.0 

2.225 

3.252 

2.59 

4.0 
6.0 
10.0 
15.0 
20.0 

2.686 
3.640 
5.600 
8.080 
10.580 

4.201 
6.143 
10.091 
15.086 
20.081 

3.21 

The  gradient  at  any  point  in  the  line  joining  the  centers  of  the 
spheres  and  distance  y  from  the  mid-point  of  this  line  is 


9 


[a?(f  +  1)  -  4tf(J  -  I)]2 
If  two  equal  spheres  are  never  separated  a  greater  distance  than 
twice  their  radii,  corona  can  never  form,  but  the  first  evidence 
of  overstress  is  spark-over.     If  the  separation  is  greater  than 
9  2R,  corona  forms  and  it  is  then  necessary  to  further  increase  the 
voltage  to  cause  spark-over.     The  condition  for  corona  or  spark- 
over  will  now  be  given.     A  wire  in  a  cylinder  will  be  taken,  as  the 
calculations  are  simpler  and  best  illustrate  the  condition. 

Condition  for  Spark-over  and  for  Local  Breakdown,  or  Corona. 
—  For  a  wire  in  a  cylinder  the  maximum  gradient,  and  thus  where 
breakdown  will  first  occur,  is  at  the  wire  surface, 


r  loge  R/r 


(6a) 


1  Dean,  Physical  Review,  Dec.,  1912,  April,  1913. 
Dean,  G.  E.  Review,  March,  1913. 

2  Distance  of  grounded  sphere  to  ground  in  these  tests  is  4  to  5  diameters. 


28 


DIELECTRIC  PHENOMENA 


When  e  is  of  such  value  that  g  at  the  wire  surface  just  exceeds 
the  breakdown  strength  of  air,  the  air  at  that  point  becomes  con- 
ducting, or  corona  forms,  thus  in  effect,  increasing  the  size  of  the 
conductor.  If  this  increase  lowers  the  gradient,  the  breakdown 
will  be  local,  and  we  say  corona  is  on  the  wire.  If  the  ratio  R/r 
is  such  that  the  increase  in  size  of  the  conductor  by  the  conduf  t- 
ing  air  increases  the  gradient,  the  broken  down  area  will  continue 
to  enlarge,  or  spark-over  will  occur.  The  condition  for  corona  or 
spark-over  may  be  found  thus: 


r  loge  R/r 

For  a  constant  value  of  e  and  R  find  the  value  of  r  to  make  g  a 
minimum 


i  / 

1/0  =  x  = 


n          D  \ 

=  -  (loge  R  -  loge  r) 


"max 


^  =  -  (log,  R  -  log,  r  -  1) 
dr       & 

=  0  for  extreme  of  x 


-    (\0ge  R    - 
€ 


0    .1    .2  .3    .4    .5  .6    .7    .8  .9  1.0 
•r 
R 


r  -  1)  =  0 

loge   R/r  =  1 
R/r  =  e 
therefore 

l/g  is  maximum  when  R/r  =  e 
or 


FIG.  12. — Concentric  cylin- 
ders.— Variation  of  gradient 
at  surface  of  inner  cylinder  as 
radius  is  changed — outer  cyl- 
inder constant. 


g  is  minimum  when  R/r   =  e 

In  other  words  the  stress  on  the  air 
decreases  with  increasing  r  until  R/r 
=  e.  When  R/r  is  equal  to  or  less 
than  e  an  increase  in  r  increases  g. 

Thus  if  R/r  ^  e  and  g  is  brought  up  to  the  rupturing  point,  g 
progressively  increases  and  spark- over  must  occur.  If  R/r  >  e 
corona  forms  and  the  voltage  must  be  still  further  increased  be- 
fore spark-over  occurs. 

This  is  illustrated  graphically  in  Fig.  12.  Note  that  this  is 
plotted  between  r/R  and  g.  Thus  the  minimum  occurs  when 
r/R  =  1/6.  It  is  interesting  to  note  here  that  with  a  given  R  a 
cable  has  maximum  strength  when  r  is  made  such  that 

R/r  =  e 
This  is  not  the  practical  ratio  however,  as  will  appear  later. 


THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT      29 


COLLECTED  FORMULAE  FOR  THE  COMMON  ELECTRODES 

Concentric  Cylinders.  : 

„       5.55/clO-13  ,       , 
Capacity  C  =     ,       R.      farads  per  cm. 

Gradient  g,  =  R/f  kv.  per  cm. 


/> 

Max.  gradient      g  =  —  j  --  gy-  kv.  per  cm. 

Corona  does  not  form  when 

R/r<  2.718 

x   =  distance  from  center  of  cylinder  in  cm. 
R  =  cm.  radius  of  outer  cylinder. 
r    =  cm.  radius  of  inner  cylinder. 

Parallel  Wires.  : 
Capacity  or  permittance  to  neutral 

5.55/clO-13  5.55&10-13 


--I 


farads  per  cm. 


Gradient  (at  x  cm.  distance  from  wire  surface  on  line  through 
centers) 


_  4r2  kv.  per  cm. 

{ (r  +  x)  (S  -  2r)  -  z2}  loge  [|-  + 

Max.  gradient  (at  conductor  surface)1 

enV\2/    ~~  ^ 

or 


^ lj  cosh"1  — 


kv.  per  cm. 


Corona  does  not  form  when 

S/r  <  5.85 
1  See  same  equations  in  different  form,  page  24.     See  formula  12c,  page  25. 


30  DIELECTRIC  PHENOMENA 

S  —  spacing  between  conductors  centers  in  cm. 
r   —  conductor  radius  in  cm. 
en  =  kv.  to  neutral. 

Equal    Spheres   in    Air. — Gradient    (non-grounded).     (At    a 
centimeters  distance  from  sphere  surface  on  line  joining  centers.) 

E     2X*[X*(f  +  1)  +  4(*  -  a)  \f  -  1)]  ] 

kv.  per  cm. 


-    1M2 


Max.  gradient  (non-grounded) 


g  =  ~  /  kv.  per  cm. 


Max.  gradient  (one  grounded) 

e      , 

®  =  ~x        per  cm< 


where        /  =  ^  +  1  +  yJ(X/R  +  I)2  +  8 

and          /o  =  see  table,  page  27. 
Corona  does  not  form  when  X/R  <  2.04 

R  =  radius  of  sphere  in  cm. 
X  =  cm.  spacing  between  nearest  surfaces. 
e    =  kv.  bet.  spheres. 
Capacity  or  permittance 

C  =  oT-7^— TT  10-11  farads. 
^  36  (/  -  1) 

Combination  of  Dielectrics  of  Different  Permittivities.— When 
several  dielectrics  of  different  permittivities  are  combined,  as  is 
usually  the  case  in  practice,  it  becomes  important  to  so  proportion 
and  shape  the  electrodes  and  insulations  that  one  dielectric  does 
not  overstress  another.  This  is  of  especial  importance  in  insu- 
lators where  dielectrically  weak  air  of  low  permittivity  is  neces- 
.  sarily  in  combination  with  dielectrically  strong  insulations  of 
high  permittivity. 

Dielectric  Flux  Refraction. — When  dielectric  flux  lines  pass 
from  a  dielectric  of  permittivity  ki  to  another  of  permittivity  of 
fc2  the  lines  are  bent  or  refracted.  This  does  not  occur,  of  course, 


THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT      31 


when  the  lines  strike  the  surfaces  normally,  as  in  a  concentric 
cable,  and  between  parallel  plates  already  considered.  The 
angle  of  refraction  bears  a  definite  relation  to  the  ratio  of  the 
two  permittivities  and  can  be  shown  as  follows: 

Let  AB,  Fig.  13,  be  the  common  surface  of  the  two  insulations. 
The  flux  ^i  makes  an  angle  0i 
with  the  normal  NN  to  the  sur- 
face. The  total  flux  through  the 
equipotential  surface  ab  is  the 
same  as  the  total  flux  through 
the  surface  cd.  The  voltage  be- 
tween a  and  c  must  be  the  same 
as  the  voltage  between  b  and  d, 
because  potential  at  a  =  poten- 
tial at  b  and  potential  at  c  =  po- 
tential at  d. 


N 


Therefore 

\t>  =  Di  ab  =  Dzcd     (14) 

In  the  uniform  field 

e  (. 

91  =  id     S2~i 

where  e  is  volts,  a  to  c  =  volts  b  to  d 

Therefore  g\bd  =  02ac 

Combining  (14)  and  (15) 

DI  ab  _  DZ  cd 
0i  bd        02  ac 


FIG.  13. — Dielectric  flux  refraction. 


(15) 


But 

Therefore 

Therefore 


D2/g2  =•  K2 


tan  0i 
tan  0i 
tan  02 


tan  02 
Ki 


Dielectric  in  Series.  —  Take  the  simple  case  of  two  parallel 
planes  with  two  different  dielectrics  between  them  and  neglect  the 
flux  concentration  at  the  edges  (Fig.  14,  flux  concentration  not 


32 


DIELECTRIC  PHENOMENA 


shown).     As*  the  lines  are  normal  to  the  electrodes  there  is  no 
refraction.     The  same  flux  passes  from  plate  to  plate. 


k^KA 


C2  = 


k2KA 


XL 

k2KA 

X2 

k^KA          k2KA 


r 

=  C2e2  = 


e2 


&1   =  — ; —  62 

e  =  ei  -f-  e2 
e  =  e»  - 


' 

,  •  }T  I 

k 

1 

X, 

i 

2 

1      t      1 

}• 

FIG.  14. — Dielectrics  of  different  permittivities  in  series. 
The  voltages  are  therefore  divided  thus 

e 


e2  = 


V  +  llkJ 


The  gradients  are 


(16) 


The  voltages  and  gradients  may  be  found  in  the  same  way  for 
any  number  of  insulations  in  series.    The  expression  for  the  gradi- 


THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT      33 
ent  at  any  point  x  in  a  combination  of  n  insulations  in  series  is: 


Q*  = 


(16a) 


Where  the  distance  between  the  electrodes  is  greater  than  the 
radius  of  the  edges  the  increase  in  stress  at  the  edges  becomes 
appreciable. 

Concentric  Cylinders. — For  concentric  cylinders  the  expression 
may  be  found  in  the  same  way.  The 
flux  lines  in  this  case  also  are  normal 
at  every  boundary  surface  and  are 
hence  not  refracted.  Consider  a  wire 
of  radius  r\  surrounded  by  n  insula- 
tions whose  inside  radii  are  respec- 
tively n,  r2,  .  .  .  rn,  and  whose  per- 
mittivities are  fci,  kz,  .  .  .  kn. 

At  the  distance  x  from  the  center  of 
the  wire,  which  falls  in  the  dielectric 
of  inside  radius  rx,  outside  radius  rx+i, 
and  permittivity  kx,  the  expression  for 
the  gradient  gx  is  found  as  follows: 

1/C  =  1/d  +  1/C2  +  .   .   .  +  l/Cx  + 


FIG.  15. 


/log. 


,    loge  r3/r2 


+ 


-l/Cn 

loge  (rx 


kx 
.  +- 


c 


+ 


/log. 

\    ) 


_L__2i_ 


3/r2  j 


logeTVH/r,  logeR/rn 

Kx  n>n 


Ce 
A 


/  loge  r2/ri  loge  r3/r2  , 

\  frl  ~T  I-    •        •        •    -I-  7 

\  A/1  A/2  ft/a; 

D, 


^+...+ 


\ogeR/r 


k 


kxK 

e 

u 

•x  /Ioger2/ri  ,  log 

;er3/r2  ,             logerz+1/ 

/r»                    ,     loge^An1 

\       A?i 

JL             T    •  •  •  T           T 
A/2                                          /vx 

'    '  '  '    '            kn        . 

(17) 


34 


DIELECTRIC  PHENOMENA 


FIG.  16. — The  refraction  of  lines  of  force  passing  through  a  porcelain 
insulator  (permittivity  assumed  4). 


FIG.  17. — Dielectrics  in  multiple. 


FIG.  18. — Rod  and  ring  with  two  di- 

FIG.     19. — Dielectrics    in   multiple    electrics.       Boundary    of    dielectrics 
and  in  series.  along  line  of  force.     (Not  drawn  to 

scale.) 


Dielectrics  in  Multiple. — Where  dielectrics  are  combined  in 
multiple,  the  division  between  the  dielectrics  being  parallel  to 
the  lines  of  force  (Fig.  17),  the  stress  on  either  is  the  same  as  it 


THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT      35 


would  be  were  the  other  not  present.  Fig.  18  shows  a  rod  in- 
sulated from  a  ring  by  a  dielectric  so  shaped  as  to  make  use  of 
this  fact.  Where  the  division  line  is  not  parallel  to  the  lines  of 
force,  some  lines  must  pass  through  both  dielectrics  (Fig.  19). 
For  these  lines  the  insulators  are  in  series,  and  the  corresponding 
precautions  are  necessary,  just  as  in  Fig.  14. 


•100K.V. 


.^Isolated 


OK.V, 


FIG.  20. — Field  not  changed  by  a  thin  insulated  metal  plate  on  an  equi- 

potential  surface. 

Flux  Control. — In  certain  electrical  apparatus  it  is  very  often 
possible  to  prevent  or  reduce  dielectric  flux  concentration  by 
superposing  fields  upon  existing  fields.  When  it  is  necessary  to 
superpose  two  fields,  as  often  happens  in  the  course  of  design,  it 
is  important  to  see  that  it  is  properly  done.  For  instance,  as  a 
simple  case,  suppose  the  two  plates.  A  and  B  in  Fig.  20,  are  at 


(a) 


-100K.V.    B. 


(b) 


50K.V. 


OK.V.    A 


\ 

50K  V 

A 

OK.V. 

FIG.  21. — (a)  Field  not  changed  if  the  potential  of  the  plate  is  the  same 
as  that  of  the  surface  upon  which  it  rests,  (b)  Field  changed  by  plate  at 
potential  different  from  the  surface. 

potentials  of  0  and  100  kv.  respectively.  A  thin  insulated  metal 
plate,  C,  may  be  placed  anywhere  between  A  and  B  without 
changing  the  field  as  long  as  it  follows  an  equipotential  surface — 
that  is,  parallel  to  A  and  B.  Unless  it  follows  an  equipotential 
surface  flux  concentration  results.  If  C  is  insulated  and  brought 
to  a  potential  of  50  kv.,  the  field  will  be  disturbed  unless  C  follows 
the  50  kv.  equipotential  surface,  or,  in  other  words,  is  midway 


36 


DIELECTRIC  PHENOMENA 


between  the  two  plates — otherwise  the  stress  in  part  of  the  in- 
sulation will  be  greatly  increased.  See  Fig.  21  (a)  and  (6). 

Fig.  21  (a)  shows  the  position  for  no  change. 

Fig.  21(6)  shows  very  great  increase  of  stress  on  part  of  the 
insulation. 

A  coil  of  wires  in  which  the  turns  are  at  different  potentials 
may  be  placed  in  the  field  with  least  disturbance  if  the  potential 
of  each  coil  corresponds  to  the  potential  of  the  equipotential 
surface  upon  which  it  rests,  as  shown  approximately  in  Fig.  22 (a). 


(a) 


1 

Q- 

-- 

-- 

i 

- 

_ 

_80     " 

Ly  J 

-- 

.- 

4- 

- 

-- 

- 

~ 

. 

-60     •• 

Ml  1 

A 

10    " 

I  I  y  J 

I 

< 

> 

--20     " 
-  0    ..       A 

LLLl 

100  K.V. 


OK.V. 


FIG.  22. — Conductors  placed  in  a  uniform  field. 


When  insulation  is  used  around  small  conductors,  points,  etc., 
the  stress  may  be  very  great.  This  stress  may  be  reduced  by 
superposing  a  uniform  field.  For  instance,  take  two  small  paral- 
lel wires  with  voltage  e  between  them,  the  stress  is 


If  a  uniform  field  is  superposed,  as  in  Fig.  22(6)  of  gradient  gi  =  «» 
the  stress  on  the  wires  becomes 

02  =  20i 

These  principles  must  be  used  in  generator  and  transformer 
design,  etc.,  and  will  be  applied  in  a  later  chapter. 

Imperfect  Electric  Elasticity. — The  electric  displacement  has 
been  shown  to  follow  Hooke's  law  by  analogy,  that  is. 

*  =  Ce 

"  -  *{£) 

or  strain  =  constant  X  stress. 

The  dielectric  has  so  far  been  assumed  to  be  perfectly  elastic. 
For  a  perfectly  electrically  elastic  material  C  or  k  must  be  con- 


THE  DIELECTRIC  FIELD  AND  DIELECTRIC  CIRCUIT      37 

stant  and  independent  of  the  time  that  the  stress  e  or  g  is  applied. 
This  appears  to  be  the  case  for  perfectly  homogeneous  dielectrics 
as  air,  various  gases,  pure  oil,  etc.,  but  is  not  so  for  non- 
homogeneous  dielectrics.  As  an  example  of  imperfectly  elastic 
dielectrics — take  a  cable;  when  potential  is  applied  between  core 
and  case  the  displacement  immediately  reaches  very  nearly  its 
full  value,  but  gradually  increases  through  an  appreciable  time 
slightly  above  its  initial  value.  It  thus  appears  that  energy  is 
slowly  absorbed  and  this  phenomenon  has,  therefore,  been  termed 
absorption.  When  the  above  condenser  is  disconnected  from  the 
supply,  and  then  short  circuited,  the  potential  difference  becomes 
zero.  If  the  short  circuit  is  removed  a  very  small  potential 
difference  gradually  reappears  as  residual.  If  such  a  condenser 
is  displaced  (charged),  and  the  supply  is  removed,  the  displace- 
ment gradually  disappears  by  conduction  or  leakage.  In  meas- 
uring the  high  voltage  d.c.  resistance  of  cable  insulation  it  is 
often  necessary  to  allow  several  minutes  to  elapse  before  the 
current  becomes  constant.  The  residual  is  analogous  to  residual 
stretch  in  an  imperfectly  elastic  metal  wire.  For  instance,  if  a 
steel  rod  is  stretched  and  the  stress  is  removed,  it  immediately 
assumes  very  nearly  its  initial  length,  but  there  is  always  very 
small  residual  stretch  which  very  gradually  disappears. 

It  has  been  shown  theoretically  that  the  phenomenon  of  ab- 
sorption should  exist  for  non-homogeneous  dielectrics,  but  not 
for  homogeneous  dielectrics. 

In  non-homogeneous  dielectrics  the  effect  of  this  residual  is 
to  cause  the  flux  to  lag  behind  the  voltage  if  the  voltage  change 
is  rapid  as  in  the  case  of  high  frequency.  This  is  analogous  to 
damping.  If  the  change  in  voltage  is  slow,  however,  the  effect 
would  not  result.  A  loop  may  thus  be  plotted  (when  the  change 
of  voltage  is  rapid)  between  voltage  and  displacement,  similar  to 
the  hysteresis  loop.  If  the  frequency  is  very  low  or  the  dielectric 
is  homogeneous  the  loop  does  not  result. 

This  loop  means  loss,  but  it  is  not  analogous  to  hysteresis  loss 
in  iron  which  is  independent  of  time. 


CHAPTER  III 
VISUAL  CORONA 

SUMMARY 

Appearance. — If  potential  is  applied  between  the  smooth 
conductors  of  a  transmission  line  or  between  concentric  cylin- 
ders and  gradually  increased,  a  voltage  is  finally  reached  at 
which  a  hissing  noise  is  heard,  and  if  it  is  dark,  a  pale  violet  light 
can  be  seen  to  surround  the  conductors.  This  voltage  is  called 
the  critical  visual  corona  point.  If  a  wattmeter  is  inserted  in  the 
line  a  loss  is  noticed.  The  loss  increases  very  rapidly  as  the  vol- 
tage is  raised  above  this  point.  The  glow  or  breakdown  starts 
first  near  the  conductor  surface,  as  the  dielectric  flux  density 
or  gradient  is  greatest  there.  As  the  broken  down  air  near  the 
surface  is  conducting,  the  size  of  the  conductor  is,  in  effect, 
increased  by  conducting  corona.  This  increases  for  the  given 
voltage  until  the  flux  density  or  gradient  is  below  the  rupturing 
gradient,  when  it  cannot  spread  any  more.  If  the  conductors 
are  very  close  together,  a  spark  strikes  between  them  immediately 
and  corona  cannot  form.  If  the  conductors  are  far  apart  corona 
forms  first,  and  then,  if  the  voltage  is  sufficiently  increased,  a 
spark  strikes  across. 

Whenever  corona  is  present  there  is  always  the  characteristic 
odor  of  ozone.  Air  consists  of  a  mechanical  mixture  of  oxygen 
(Oz)  and  nitrogen  (N).  When  air  is  overstressed  electrically 
the  oxygen  molecule  is  split  up  into  O,  when  it  becomes  chemically 
very  active.  The  atoms  again  combine  by  the  law  of  probability 

O 
into  O  =  O,  (O2),  the  normal  state,  and   /\  ,  (O3)  or  ozone. 

O O 

Oxygen  in  the  nascent  state  (O)  also  combines  with  metal,  organic 
matter,  etc.,  if  such  are  present.  Ozone  is  also  not  stable  and  is, 
hence,  chemically  active;  it  splits  up  as  Q%  and  O  when  the  latter 
combines  readily  with  metals,  and  organic  matter.  If  the  electrical 
stress  is  very  high  the  oxygen  enters  into  chemical  combination 
with  the  nitrogen,  forming  oxides.  The  energy  loss  by  corona  is 
thus  in  a  number  of  forms,  as  heat,  chemical  action,  light,  noise, 
convection,  etc. 

A.C.  and  D.C.  Corona. — When  alternating  voltage  higher  than 
the  critical  voltage  is  applied  between  two  parallel  polished  wires, 

38 


FIG.  23. — A.  C.  corona  on  polished  parallel  wires. 


FIG.  24. — Corona  on  parallel  wires.  Iron.  First  polished  and  then  oper- 
ated at  120  kv.  for  two  hours  to  develop  spots.  Diameter,  0.168  cm. 
Spacing,  12.7  cm.  Stroboscopic  photo.,  80  kv.-60  ~. 

(Facing  page  38.) 


Wire  "dead". 


FIG.  25. — D.  C.  corona  on  smooth  wires  by  Watson.  .  (See  Fig.  79.) 


VISUAL  CORONA  .       39 

the  glow  is  quite  even,  as  shown  in  Fig.  23.  After  operation  for 
a  short  time  reddish  beads  or  tufts  form  along  the  wire,  while 
around  the  surface  of  the  wire  there  is  a  bluish-white  glow.  If 
the  conductors  are  examined  through  a  stroboscope,  so  that  one 
wire  is  always  seen  when  at  the  positive  half  of  the  wave,  it  is 
noticed  that  the  reddish  tufts  or  beads  are  formed  when  the  con- 
ductor is  negative  and  the  smoother  bluish-white  glow  when  the  • 
conductor  is  positive.  (See  Fig.  24.)  A.c.  corona  viewed  through 
the  stroboscope  has  the  same  appearance  as  d.c.  corona.  (See 
Fig.  25,  d.c.  corona.)  The  d.c.  corona  on  the  +  wire  has  exactly 
the  same  appearance  as  the  a.c.  corona  on  the  +  half  of  the 
wave;  the  same  holds  for  the  —  wire. 

Measure  of  Stress. — The  gradient  in  kilovolts  per  centimeter  is 
a  measure  of  the  stress  on  the  dielectric.     For  parallel  wires  the 
gradient  at  the  wire  surface,  and  hence  where  the  stress  is  a  maxi- 
mum and  where  the  " dielectric  elastic  limit"  is  first  exceeded,  is 
de  e 

dx  ~~  g  ~  r  loge  S/r 

That  is,  if  the  voltage  between  the  surface  of  the  conductors 
and  a  point  in  space  at  infinitesimal  distance  dx  cm.  away  is  de, 
then  this  gradient  in  the  limit  at  the  surface  is 
de  e 

dx  ~~~  g  ~  r  loge  S/r 

If  e  is  ev,  the  observed  voltage  to  neutral  at  which  visual  corona 
starts,  gv  is  a  measure  of  the  stress  at  breakdown.  For  a  wire  in 
the  center  of  a  cylinder 

ev 
r  loge  R/r 

Influence  of  Wire  Spacing  and  Diameter  on  Apparent  Strength 
of  Air. — If  the  visual  corona  voltages  are  measured  for  a  given 
conductor  at  various  spacings,  it  is  found  that  gv;  or  the  apparent 
strength  of  air,  is  a  constant  independent  of  the  conductor  spacing. 
It  would  also  naturally  be  expected  that  gv  would  be  a  constant 
for  all  conductors  independent  of  their  diameter,  or  in  other  words, 
air  would  break  down  under  the  same  constant  unit  stress  inde- 
pendent of  the  size  of  the  conductor;  just,  for  instance,  as  differ- 
ent sized  rods  of  the  same  material  would  be  expected  to  break 
down  at  the  same  unit  stress  of  kilograms  per  square  centimeter. 
It  has  long  been  known,1  however,  that  air  is  apparently  stronger  at 

1  Ryan,  The  Conductivity  of  the  Atmosphere  at  High  Voltage,  A.I.E.E., 
Feb.,  1904. 


40  DIELECTRIC  PHENOMENA 

the  surface  of  small  conductors  than  large  ones.  (The  measured 
apparent  strength  curve  is  given  in  Fig.  28.)  Of  course  this  does 
not  mean  the  voltage  required  to  start  corona  is  greater  for  small 
wires  than  for  large  ones  (it  is  lower  for  the  small  conductors  at  a 
given  spacing),  but  that  the  term  gv,  or  unit  stress  in  the  expression 

ev  =  gvr  loge  S/r 
is  greater  for  air  around  small  conductors  than  large  ones. 

This  apparently  greater  strength  of  air  around  small  conductors 
was  long  attributed  to  a  film  of  condensed  air  at  the  conductor 
surface,  because  such  a  film  would  have  a  greater  relative  effect 
for  the  smaller  conductors.  We  have  given  another  reason 
for  this  which  experiments  at  low  air  densities  seem  to  confirm. 
During  our  first  investigations  we  found  that  the  relation  between 
the  apparent  strength  of  air  and  the  radius  of  the  conductor  could 
be  expressed  by  the  simple  formula 


where  g0  is  a  constant  and  is  about  30  kv.  per  centimeter.1  This 
means  that  the  stress  at  the  conductor  surface  at  breakdown  is 
not  the  same  for  all  diameters,  as  already  stated,  but  always 
constant  at  a  distance  0.301V7  cm.  from  the  surface.  (See  Fig. 
29.)  This  follows: 

/1        0.301  \  e, 

gv  =  H   "  3Ty  =  MO^A 

therefore,  g.  =  (r  +  ^^  loge  s/r 

The  gradient  x  cm.  from  center  of  the  conductor  is  approxi- 
mately 

a  =         6v 
g       x  loge  S/r 

x  =  (r  +  0.301VV) 

therefore,  g0  is  the  gradient  0.301\/r  cm.  from  surface.  There- 
fore, by  substitution  also 

(0  301  \ 
1  +  -  '  /-   )r  loge  S/r  max.  kilovolts  to  neutral 
V  r  I 

or  for  a  sine  wave 

ev  =  21.2(l  +  -17^)r  loge  S/r  kilovolts  effective  to  neutral  (19) 
V         V  r  I 

1  F.  W.  Peek,  Law  of  Corona,  A.I.E.E.,  June,  1911. 


VISUAL  CORONA  41 

The  visual  corona  voltage  for  any  diameter  of  wire  at  any 
spacing  may  thus  be  calculated. 

The  explanation  seems  to  be  this:  Air  has  a  constant  strength 
g0  for  a  given  density,  but  a  finite  amount  of  energy  of  some  form 
is  necessary  to  cause  rupture  or  to  start  corona.  It  is  obvious 
that  this  definite,  finite  energy  is  necessary,  as  evinced  by  appear- 
ance of  heat,  that  higher  transient  voltages  are  necessary,  etc. 
This  will  be  more  fully  discussed  later.  Hence  the  stress  at  the 
conductor  surface  must  exceed  the  elastic  limit  g0)  or  be  increased 
to  gv  in  order  to  supply  the  necessary  rupturing  energy  between 
the  conductor  surface  and  finite  radial  distance  in  space  away 
(0.301\/7*  cm-)  where  the  stress  is  g0,  and  breakdown  occurs. 

Application  of  the  Electron  Theory. — The  electron  theory  may 
also  be  applied  in  agreement  with  the  above.  Briefly: 

When  low  potential  is  applied  between  two  conductors  any 
free  ions  in  the  field  are  set  in  motion.  As  the  potential  and, 
therefore,  the  field  intensity  or  gradient  is  increased  the  velocities 
of  the  ions  increase.  At  a  gradient  of  g0  =  30  kv./cm.  (5  =  1) 
the  velocity  of  the  ions  becomes  sufficiently  great  over  the  mean 
free  path  to  form  other  ions  by  collision  with  molecules.  This 
is  the  property  of  the  negative  ion  or  electron.  This  gradient  is 
constant  and  is  called  the  dielectric  strength  of  air.  When 
ionic  saturation  is  reached  at  any  point  the  air  becomes  con- 
ducting, and  glows,  or  there  is  corona  or  spark. 

Applying  this  to  a  wire  in  the  center  of  a  cylinder:  When  a 
gradient  gv  is  reached  at  the  wire  surface  any  free  ions  are  acceler- 
ated and  produce  other  ions  by  collision  with  atoms  or  molecules, 
which  are  in  turn  accelerated.  The  ionic  density  is  thus  gradually 
increased  by  successive  collisions  until  at  0.301\/r  cm.  from  the  wire 
surface,  where  g0  =  30,  ionic  saturation  is  reached,  or  corona  starts. 
The  distance  0.301\/^  cm.  is  of  course  many  times  greater  than  the 
mean  free  path  of  the  ion  and  many  collisions  must  take  place 
in  this  distance.  Thus,  for  the  wire,  corona  cannot  form  when  a 
gradient  of  g0  is  reached  at  the  surface,  as  at  any  distance  from 
the  surface  the  gradient  is  less  than  g0.  The  gradient  at  the  sur- 
face must,  therefore,  be  increased  to  gv  so  that  the  gradient  a 
finite  distance  away  from  the  surface,  0.301\/^  cm.,  is  g0.  This 
is  the  same  as  saying  that  energy  is  necessary  to  start  corona,  and 

<\ 

this  energy  is  the  S-^r-  of  the  energy  of  the  moving  ions  necessary 

a 

to  produce  ionic  saturation. 


42  DIELECTRIC  PHENOMENA 

Very  Small  Spacings  or  Films.  —  If  conductors  are  placed  closer 
together  than  this  necessary  free  accelerating  or  energy  storage 
distance,  0.301\/r  cm.,  the  rupturing  force  or  gradient  must  be 
increased.  This  will  be  better  illustrated  by  later  experiments, 
in  which  at  small  spacings  air  has  been  made  to  withstand  gradi- 
ents as  high  as  200  kv.  per  centimeter. 

Air  Density.  —  Thus  far  the  discussion  has  been  limited  to  air 
at  a  constant  density,  or,  in  other  words,  constant  pressure  and 
temperature.  The  above  energy  explanation  can  be  still  further 
checked  by  considering  air  at  different  densities.  The  value 
of  g0  given  is  for  air  density  at  sea  level  (25  deg.  C.,  76  cm.  barom- 
eter). This  has  been  taken  as  the  standard,  or  for  the  density 
factor  5  =  1.  Air  at  other  densities,  due  to  change  in  tempera- 
ture and  barometric  pressure,  is  expressed  as  a  fraction  of  this. 
The  relative  density  for  any  temperature  or  pressure  is 

3.926 
273  +  t 

For  instance,  if  the  temperature  is  kept  at  25  deg.  C.  and  pressure 
is  reduced  to  38  cm. 

3.92  X  38 
:    273  +  25   = 

or  1/2  atmosphere.  As  the  air  density,  or  5  is  decreased,  the  air 
is  less  able  to  resist  the  electric  stress  at  the  increased  molecular 
spacing.  Theoretically  the  strength  of  the  air  g0  in  bulk  between 
parallel  planes  should  decrease  directly  with  5. 

g0  =  305 

gv,  however,  the  apparent  strength  of  air  in  a  non-uniform  field, 
if  the  energy  theory  is  true,  cannot  decrease  directly  with  5: 
the  energy  storage  distance  should  be  0.301  vW  (5),  or  the  com- 
plete expression  should  take  the  form 

0.301 


We  have  found  experimentally  that  the  energy  storage  distance 
a  =  0.301  ~~  cm.;  that  is,  gv  =  305^1+  ° 


~~        .  ,    v 

V5  \          V5r/ 

The  electron  theory  may  also  be  applied  here: 


VISUAL  CORONA  43 

00,  the  strength  of  air,  varies  directly  with   5.     gv,  however, 
cannot  vary  directly  with  <5  because  with  the  greater  molecular 
spacing  or  mean  free  path  of  the  ions  at  lower  air  densities,  a 
greater   "accelerating"   distance  is  necessary  in  the    equation 
a  =  0.301  VV/5  that  is,  "a"  increases  with  decreasing  5.     This 
is  shown  experimentally  by  sphere  gap  tests. 
For  parallel  planes  r   =   °o 
•  •  Qv.=  g0ft)  as  expected. 

The  equation  for  the  visual  critical  corona  voltage  may  now 
be  written: 

ev  =  gv8r  loge  S/r  =  g05(l  +  °^  }r  loge  S/r  kv.       (20) 


where  ev  is  Kv    to  neutral.     g0  =  30    for  max.,   g0  =  21.1    for 
effective  sine  wave. 

It  may  be  of  interest  to  note  that  with  a  pair  of  smooth  wires, 
of  a  known  diameter,  high  voltages  may  be  accurately  measured 
anywhere  by  noting  the  spacing  at  which  corona  starts,  the  tem- 
perature and  barometric  pressure,  and  substituting  in  the  above 
formula. 

The  various  other  factors  affecting  visual  corona  will  be 
mentioned. 

Conductor  Surface  —  Cables  —  Material.  —  For  rough  or  weath- 
ered conductors  corona  starts  at  lower  voltages.  This  is  taken 
care  of  by  the  irregularity  factor,  mv.  For  cables  and  weathered 
wires  the  complete  formula  becomes 

ev  =  mvSgv  r  loge  S/r 

For  the  same  surface  condition  the  starting  point  is  independent    \/ 
of  the  conductor  material. 

Oil  and  Water,  Current  in  the  Conductor,  Wave  Shape,  Etc.  — 
Water,  sleet  and  snow  lower  the  visual  corona  voltage. 

Oil  on  the  conductor  surface  has  very  little  effect. 

Humidity  has  no  effect  upon  the  starting  point  of  visual  corona. 

Initial  ionization  over  a  considerable  range  has  no  appreciable     • 
effect  at  commercial  frequencies. 

Current  in  the  wire  has  no  effect  except  that  due  to  heating  of 
the  conductor  and  surrounding  air. 

Wave  Shape.  —  The  corona  point  at  commercial  frequencies 
depends  upon  the  maximum  value  of  the  wave.  When  results 
are  given  in  effective  volts  a  sine  wave  is  assumed.  With  peaked 
wave,  corona  starts  at  a  lower  effective  voltage  than  with  a 


44 


DIELECTRIC  PHENOMENA 


Shield  for  Small  Wire 


Shield  for  Large  Wire 


O 


\ 


o 


flat-top  wave.  D.c.  corona  starts  at  a  value  corresponding  to 
the  maximum  of  the  a.c.  wave  or  41  per  cent,  higher  than  the 
effective  a.c.  critical  voltage.1  See  appendix  for  further  data. 

The  above  summary  will  now  be  taken  up  more  in  detail  and 
experimental  proof  given. 

EXPERIMENTAL  STUDY  OF  VISUAL  CORONA 

Effect    of    Spacing    and    Size    of    Conductor.— The    visual 
critical  voltage,  or  voltage  at  which   visual   corona   starts  on 

polished  conductors  of  a  given 
diameter  and  spacing,  at  con- 
stant air  density,  can  be  repeat- 
edly checked  within  a  small  per 
cent.  Visual  tests  were  made 
on  two  parallel  polished  con- 
ductors supported  indoors  on 
wooden  wheels  in  a  wooden 
framework.  The  wires  were 
not  allowed  to  come  directly 
in  contact  with  the  wood  but 
rested  on  aluminum  shields. 
(See  Fig.  26.)  The  object  of 
the  shields  was  to  prevent  the 
glow  at  low  voltages  which 
would  take  place  if  the  wires 
came  in  contact  with  the  wood. 
The  tests  were  made  in  a  dark 
room,  and  method  of  procedure 
was  as  follows:  Conductors  of 
a  given  size  were  placed  upon  a 
framework;  voltage  was  applied 
and  gradually  increased  until 
the  visual  critical  corona  point  was  reached.  Critical  points 
were  taken  at  various  spacings  and  recorded  as  in  Table  I. 
Unless  otherwise  stated  tests  were  made  at  60  ^. 

As  the  visual  critical  voltage,  ev,  is  the  voltage  at  breakdown 
of  the  air,  the  surface  gradient  corresponding  to  this  voltage  must 
be  the  stress  at  which  air  ruptures.  This  is  called  the  visual 
critical  gradient  gv.  Where  the  wires  are  far  apart  or  S/r  is  large 


o 


FIG.  26. — Wire  support  for  visual 
corona  tests. 


de 
dr 


=  gv  = 


€v 


r  logc  S/r 

1  Peek,  The  Effect  of  High  Continuous  Voltages  on  Air,  Oil  and  Solid 
Insulation,  A.I.E.E.,  June,  1916. 


VISUAL  CORONA 


45 


where 

ev  =  the  (maximum)  voltage  to  neutral. 

r    =  radius  of  the  conductor  in  cm. 

S  =  distance  between  centers  of  conductors  in  cm. 
Values  of  gradient  calculated  for  a  given  conductor  at  various 
spacings  are  given  in  Table  I.  (See  Fig.  27.)  It  is  seen  that  the 
breakdown  gradient  is  constant,  or  independent  of  the  spacing. 
This  test  was  repeated  for  various  diameters.  The  values  of  the 
gradients  are  tabulated  in  Table  II  and  plotted  in  Fig.  28. 


Critical  Gradient  fft>-K  Vcrn 

sis 

8  en 

• 

• 

* 

* 

M70 

, 

'S 

i 

u 
•3 

50 

Spacing.  S_  cm 

(a) 

FIG.  27 (a). — Variation  of  visual 
critical  gradient  with  spacing. 
(Parallel  wires.  Diameter  constant 
=  0.034  cm.) 


100  .2 


5  10 

o  Radius  of  Outer  Cylinder  -R-cm 

(b) 

FIG.  27 (b). — Variation  of  visual  crit- 
ical gradient  with  radius  of  outer  cyl- 
inder. (Concentric  cylinders.  Diam- 
eter of  inner  wire  constant  =  0 . 1 18  cm. ) 


TABLE  I. — VISUAL  CRITICAL  VOLTAGES  AND  gv  WITH  VARYING  SPACING  AND 

CONSTANT  DIAMETER 
(Polished  Parallel  Copper  Conductors — Diameter  0.0343  cm. — 60  ~) 


«  cm. 

evl  kilovolts  between  con- 
ductors (effective) 

evl  kilovolts  between  con- 
ductors (maximum) 

Ov  kv./cm. 
(maximum) 

2.54 

12.1 

17.0 

99.5 

2.93 

12.4 

17.4 

99.0 

3.18 

12.5 

17.7 

98.5 

3.81 

13.0 

18.4 

99.0 

4.45 

13.5 

19.0 

99.5 

5.08 

13.8 

19.4 

100.0 

5.73 

14.0 

19.8 

99.0 

7.62 

14.5 

20.5 

99.0 

15.   2 

16.0 

22.6 

97.2 

30.  5 

17.7 

25.0 

97.2 

45.   6 

18.7 

26.3 

96.1 

61.  0 

19.4 

27.4 

98.0 

106.  8 

20.6 

29.0 

97.2 

Average,                     99  .  0 

46 


DIELECTRIC  PHENOMENA 


TABLE  II. — VARIATION  OF  gv  WITH  DIAMETER  OF  CONDUCTORS 

(Average  Values  for  Polished  Parallel  Wire.     60  ~.     Corrected  to  25  deg.  C. 

76  cm.  Barometric  Pressure) 


Diameter, 
cm. 

de 
dr  =  9° 
kv./cm. 
(maximum) 

Material 

Diameter, 
cm. 

de 
dr  =  g* 
kv./cm. 
(maximum) 

Material 

0.0196 

116 

Tungsten 

0.2043 

59.0 

Copper 

0.0343 

99 

Copper 

0.2560 

57.0 

Aluminum 

0.0351 

94 

Copper 

0.3200 

54.0 

Copper 

0.0508 

84 

Aluminum 

0.3230 

50.5 

Copper 

0.0577 

82 

Aluminum 

0.5130 

49.0 

Copper 

0.0635 

81 

Tungsten 

0.5180 

46.0 

Copper 

0.0780 

76 

Copper 

0.6550 

44.0 

Copper 

0.0813 

74 

Copper 

0.8260 

42.5 

Copper 

0.1637 

64 

Copper 

0.9280 

41.0 

Copper 

0.1660 

64 

Iron 

120 
110 
100 

?90 

Jso 

|70 

^60 

o 

I60 

1  40 

J  30 
*20 
10 

f 

Visual  Critical  Gradient 
Two  Parallel  Wires 
ffv=at  76  cm  B  and   25°CT  »  29.8  (l  -f  .301  *\ 
gv  =  Voltage   Gradient  kv/cm          ~^r  ' 

\ 

\ 

\ 

'X. 

o 

>-> 

"-•^ 

o-  —  . 

—  0- 

- 

~e  — 

^rr 

_ 

-  

-.-    .^-M 

555= 

.4     .5    .6     .7    .8     .9     1.0   1.1   1.2    L3   1.4  1.5    1.6  1.7  L8    1.9  2:0 

Diameter  in  cms 


0     .1    .2 

FIG.  28. — Variation  of  visual  critical  gradient  with  size  of  wire. 


The  gradient  at  breakdown  at  the  conductor  surface  is  not 
constant  with  varying  diameters,  but  increases  with  decreasing 
diameters  of  conductors — in  other  words,  air  is  apparently 
stronger  at  the  surface  of  small  wires  than  large  ones. 

The  apparent  increase  in  the  dielectric  strength  of  air  surround- 
ing small  conductors  was  explained  some  years  ago  as  due  to  a 
condensed  air  film  at  the  surface  of  the  conductor.  If  this  were 
so,  a  higher  critical  gradient  would  be  expected  for  tungsten  than 
for  aluminum.  That  is,  the  air  film  should  be  denser  around  the 


VISUAL  CORONA  47 

denser  metals.  These  experiments  show  that  the  gradient  is 
not  affected  by  the  material  or  density  of  the  conductor.  Ryan1 
has  also  explained  the  apparent  increase  by  the  electron  theory. 
The  explanation  first  offered  in  Law  of  Corona  I,2  and  already 
outlined  in  this  chapter,  will  now  be  given  more  in  detail  :  Assume 
that  air  at  a  given  density  has  a  constant  strength  g0,  but  that  a 

777  1) 

finite  amount  of  energy,  be  this  energy  the  S  -=-  of  the  moving 

ions  or  whatever  form  it  may,  is  necessary  to  cause  rupture  or 
start  corona.  Then  the  stress  at  the  conductor  surface  must 
exceed  the  elastic  limit  g0,  or  be  increased  to  gv  in  order  to  supply 
the  rupturing  energy  between  the  conductor  surface  and  a  finite 
radial  distance  in  space  where  the  stress  is  g0  and  breakdown 
occurs,  or,  in  other  words,  a  finite  thickness  of  insulation  must  be 
under  a  stress  equal  to,  or  more  than  g0. 

Just  before  rupture  occurs  the  gradient  at  the  conductor  sur- 
face is 


the  gradient  a  cm.  away  from  the  surface  is 

g 

"'  =  (r  +a)  log.  S/r 
Theoretically,  one  is  also  led  to  believe 

a  =  cf>(r) 

g°  =  (r  +  *(r»log.S7r  (23) 

It  now  remains  to  test  this  out  experimentally  and  find  </>(r). 
The  equation  of  the  experimental  curve  is  found  to  be: 

/          0.301\ 
g.v  =  g0  (1  +  a/Vf)  =  29.8(1  +  -^-J  (24) 

Substituting  (24)  in  (21) 

030JA 

" 


(r  +  0.301  Vr)  loge  S/r 
Thus  the  experimental  values  bear  out  the  above  theory 

a  =  0(r)  =   O.SOlVr 
g  =  29.8  =  constant 

1  A.I.E.E.,  January,  1911.    See  also  papers  by  Whitehead,  A.I.E.E.,  June, 
1910,  1911,  etc. 

2A.I.E.E.,  June,  1911. 


48 


DIELECTRIC  PHENOMENA 


That  is,  at  rupture  the  gradient  a  finite  distance  away  from  the 
conductor  surface,  which  is  a  definite  function  of  r,  is  always 
constant,  (See  Fig.  29.) 


01 
gv  =  29.81  1 


0.301  \ 

f=-  }  kv.  per  cm. 

Vr  / 


A  similar  investigation  made  on  wires  in  the  centers  of  metal 
cylinders  (see  Figs.  27  and  30)  shows  as  above  that  the  visual 


y 
FIG.  29. — gv  and  g0  for  small  and  large  wires. 

critical  gradient,  gv,  increases  with  decreasing  radius  r,  of  the 
wire,  but  is  independent  of  the  radius  R,  of  the  outer  cylinder. 
The  relation  between  r  and  gv  is  given  in  Table  V.  For  a  wire  in 
the  center  of  a  cylinder  the  gradient  g0  is  slightly  higher 
than  for  similar  parallel  wires,  apparently  due  to  the  fact  that 
the  field  is  everywhere  balanced  for  a  wire  in  the  center  of  a 


FIG.  30. — Apparatus  for  determining  the  visual  corona  voltage  in  con- 
centric cylinders. 

cylinder,  which  is  not  the  case  for  parallel  wires.  The  expression 
for  the  apparent  strength  of  air  for  a  wire  in  the  center  of  a  cylin- 
der is 

gv  =  31  (  1  +  -  '—T=-  }   kv.  per  cm. 

\  V  r  / 

It  thus  seems  that  gc  =  31  is  the  true  dielectric  strength  of  air. 


VISUAL  CORONA 


49 


The  method  of  reducing  the  results  to  equations  was  as  follows : 
Various  functions  of  r  and  gv  were  plotted  for  parallel  wires  from 
Table  II,  until  it  was  found  that  a  straight-line  law  obtained 
between  gv  and  l/\/?I  All  values  of  gv  and  \/\fr  were  then  tabu- 
lated as  in  Table  III  and  plotted  as  in  curve  (Fig.  31).  Points 


Qv  Kilovolts  per  cm.  ~- 

8  g  §  S  8  § 

^ 

s^* 

^ 

^ 

^ 

^f 

? 

^> 

>^ 

j^ 

•^ 

^ 

' 

Visual  Oriti 
Method  of  Re 
between 

3al  Gradie 
lucing  Eela 
7,,  and  r 

at 

4$ 

^ 

^ 

01234        5        6         78         9        10 


FIG.  31. — Relation  between  gv  and  — 7=' 

Vr 


TABLE  III. — RELATION  OF  VISUAL  CRITICAL  VOLTAGE  GRADIENT 
TO  RADIUS 

(Experimental  Values  Corrected  to  76  cm.  Barometer  and  25  deg.  C.  Parallel 

Wires  60  ~) 


Qv 

l 

0v 

1 

Diameter, 

kv./cm. 

Radius, 

vf 

Diameter, 

kv./cm. 

Radius, 

V'T 

cm. 

(max.) 

r  =  cm. 

cm. 

cm. 

(max.) 

r  =  cm. 

cm. 

0.0196 

116.0 

0.0098 

10.10 

0.202 

59.1 

0.101 

3.13 

0.0343 

99.0 

0.0172 

7.65 

0.257 

56.7 

0.128 

2.76 

0.0350 

94.0 

0.0175 

7.58 

0.320 

54.3 

0.160 

2.51 

0.0508 

84.0 

0.0254 

6.27 

0.322 

49.6 

0.161 

2.51 

0.0577 

81.5 

0.0288 

5.90 

0.513 

48.8 

0.256 

2.01 

0.0635 

81.0 

0.0317 

5.64 

0.518 

44.5 

0.259 

1.94 

0.078 

76.0 

0.0390 

5.08 

0.655 

43.7 

0.327 

1.82 

0.0813 

73.5 

0.0406 

4.96 

0.826 

42.2 

0.413 

1.57 

0.1635 

63.8 

0.0818 

3.51 

0.928 

40.6 

0.464 

1.44 

0.1660 

63.4 

0.0830 

3.45 

varying  widely  from  the  average  straight  line  were  then  discarded 
as  probably  in  experimental  error.  The  remaining  points  were 
then  divided  into  two  equal  groups  and  tabulated  as  in  Table  IV. 


50 


DIELECTRIC  PHENOMENA 


TABLE  IV. — RELATION  OP  gv  AND 
(Showing  2A  Reduction) 


l 

1 

0, 

Vr 

ffv 

Vr 

99 

7.65 

59.0 

3.13 

82 

5.90 

54.0 

2.51 

81 

5.64 

50.5 

2.51 

76 

5.08 

49.0 

2.01 

74 

4.96 

41.0 

1.44 

2412 

S29.23 

2253.5 

211.60 

lv  =  158.5 
220r  =  665.5 

Cl 


158.5 


A2  — 7=  =  17.63 
Vr 


22^=  =  40.83 


665.5  -  (9  X  40.8) 
g   =  77 =  29.8 


Therefore : 


29.8 


29.8 


10 
9 

Vr 


,) 


In  order  to  give  proper  weight  to  the  points  the  SA  method  was 
used  in  the  evaluations  of  the  constants  for  the  equation 
above.  This  method  of  reduction,  which  is  self  explanatory,  is 
very  convenient  and  especially  suitable  where  a  large  number  of 
experimental  points  have  been  obtained,  in  which  case  the  results 
are  as  reliable  as,  or  more  so,  than  when  few  points  are  taken  and 
the  unwieldy  method  of  least  squares  used. 

Temperature  and  Barometric  Pressure. — The  density  of  the 
air  varies  directly  with  the  pressure,  and  inversely  as  the  absolute 
temperature.  In  these  investigations  the  air  density  at  a  tem- 
perature of  25  deg.  C.  and  a  barometric  pressure  of  76  cm.  has 
been  taken  as  standard.  If  the  air  density  at  this  temperature 


VISUAL  CORONA  51 

and  pressure  is  taken  as  unity,  the  relative  density  at  other  tem- 
peratures and  pressures  may  be  expressed  in  terms  of  it,  thus: 

0.004656 
:   273  +  * 

where  w  =  the  weight  of  air  in  grams  per  cubic  centimeter 

b    =  barometric  pressure  in  centimeters 
t    =  temperature  in  degrees  centigrade. 

At  25  deg.  C.  and  76  cm.  pressure 
0.00465  X  76 

W25°  -  76cm.    =    273   +  25          =    °-°°118 

w  at  any  other  temperature  and  pressure  is 

0.004656 
Wtb  =  273T* 
wtb  0.004656  3.926 


w>26°  76cm.        (273  +  00.001185       273  +  t 

3.926 
=  (273+0 

On  the  theory  that  definite  energy  is  necessary  to  start  dis- 
ruption or  glow,  g0  should  vary  directly  with  the  air  density 
factor  6;  gv,  however,  should  not  vary  directly  with  5,  as  the 
thickness  of  the  energy  or  ionizing  film  should  also  be  a  function 
of  5.  The  equation  for  gv  should  take  the  form 

(25) 


Whether  6  is  varied  by  change  of  temperature  or  air  pressure 
the  effect  should  be  the  same  as  long  as  the  temperature  is  not 
so  high  that  the  air  is  changed  or  affected  by  the  heat,  as  ioniza- 
tion,  etc. 

Temperature.  —  A  series  of  experiments  on  visual  corona  was 
carried  on  over  a  temperature  range  of  —20  deg.  C.  to  140  deg.  C.' 
The  apparatus  is  shown  in  Fig.  30.  It  consists  of  a  polished  wire 
in  the  center  of  a  brass  cylinder.  The  cylinder  was  placed  hori- 
zontally in  a  large  asbestos  lined  "hot  box,"  heated  by  grids  at 
the  bottom.  In  order  to  get  uniform  temperature  the  cylinder 
was  shielded,  and  time  was  allowed  to  elapse  after  each  reading. 
Temperature  was  observed  by  a  number  of  thermometers  dis- 
tributed in  the  hot  box. 


52 


DIELECTRIC  PHENOMENA 


TABLE  V. — RELATION  OF  VISUAL  CRITICAL  VOLTAGE  GRADIENT  TO  RADIUS 
(76  cm.  Barometer — 25  deg.  C. — Concentric  Cylinders) 


Radius 

a.c. 

R 

d.c.1 

a.c. 

R 

d.c. 

r  cm. 

r  cm. 

kv./cm. 
(max.) 

cm. 

kv./cm. 

kv./cm. 
(max.) 

cm. 

kv./cm. 

CO 

0.059 

70.4 

»o 

69.0 

0.327 

48.1 

CO 

42.0 

0.103 

60.7 

co 

59.5 

0.476 

44.9 

8 

39.0 

0.127 

58.4 

eo 
i 

55.5 

0.794 

41.9 

i 

0.129 

56.6 

1 

54.5 

0.953 

41.2 

* 

0.190 

52.7 

*0 

49.5 

1.113 

39.7 

3.81 

0.199 

52.7 

1 

48.5 

1.270 

39.2 

3  81 

0.206 

51.6 

3 

47.5 

1.588 

38.4 

3  81 

0.254 

49.9 

00 

44.5 

1.905 

37.8 

3.81 

0.318 

47.1 

43.0 

2.540 

35.0 

After  the  heating  became  uniform,  voltage  was  applied  and 
gradually  increased  until  the  glow  appeared.  The  central  con- 
ductor was  observed  through  a  window  placed  in  the  front  part 
of  the  box  so  that  the  whole  length  of  the  conductor  could  be  seen. 
It  was  found  that  it  made  no  appreciable  difference  in  the  starting 
voltage  whether  or  not  the  box  and  tube  were  "aired  out"  after 
each  test. 

Three  sizes  of  brass  cylinders  were  used  having  inside  radii  of 
8.89,  5.55,  and  3.65  cm.  respectively.  The  central  conductors 
ranged  in  size  from  0.059  to  0.953  cm.  radii.  Tables  VI  and  VII 
are  typical  data  tables. 

TABLE  VI. — VARIATION  OF  STRENGTH  OF  AIR  WITH  TEMPERATURE 

For  Polished  Copper  Tube  Inside  of  Brass  Cylinder 
r  =  0.953  R  =  5.55  cm.  Tests  at  60  ~ 


Observed  values 


Kv. 

effective 

Temp. 
C° 

6  cm. 

s 

0*(max.) 

0'»(max.) 

48.5 

18 

75.4 

1.016 

40.7 

41.4 

46.5 

37 

75.4 

0.954 

39.1 

39.1 

45.2 

50 

75.4 

0.915 

38.0 

37.7 

43.4 

66 

75.4 

0.873 

36.5 

36.2 

41.0 

85 

75.4 

0.826 

34.5 

34.5 

39.6 

100 

75.4 

0.793 

33.3 

33.3 

37.6 

119 

75.4 

0.754 

31.6 

31.9 

Calculated  from  equation 


1  D.c.  values  from  Watson,  Jour.  I.  E.  E.,  June,  1910,  Fig.  21. 

Some  investigators  have  found  a  maximum  difference  of  6  per  cent, 
between  the  (+)  and  (  — )  corona  starting  voltages.  The  difference  is 
generally  small  and  there  is  usually  fair  agreement  between  d.c.  and  max. 
a.c.  See  additional  data  in  appendix. 


VISUAL  CORONA 


53 


TABLE  VII. — VARIATION  OF  STRENGTH  OF  AIR  WITH  TEMPERATURE 

For  Polished  Copper  Tube  Inside  of  Brass  Cylinder 
r  =  0.476  cm.  R  =  5.55  cm.  Tests  at  60  ~ 


Observed  values 

Calculated  from  equation 

Kv. 

effective 

t 

6 

0»(max.) 

(/'.(max.) 

41.0 

-13 

75.5 

1.139 

49.6 

50.0 

40.0 

0 

75.5 

1.084 

48.3 

48.0 

37.0 

20 

74.9 

1.001 

44.8 

44.9 

35.7 

41 

75.5 

0.942 

43.2 

42.7 

33.2 

70 

75.5 

0.863 

40.1 

39.7 

31.5 

87 

75.5 

0.823 

38.1 

38.1 

29.5 

121 

75.5 

0.753 

35.7 

35.4 

28.7 

130 

75.5 

0.734 

34.7 

34.7 

Columns  1,  2  and  3  give  observed  values.     The  gradient  at  the 
surface  of  the  inner  cylinder  is 

_         e 
~  r  loge  R/r 

Column  5  gives  the  surface  gradient  for  the  voltage,  evt  calculated 
directly  from  observed  values.  It  can  be  seen  from  the  data, 
that  gv  for  a  given  r,  varies  with  6,  but  is  independent  of  R  or  S. 
By  SA  reduction  of  all  of  the  data  the  following  equations 
connecting  gv  with  r  and  6  were  obtained: 


80 


"40 

M'20 
10 
0 


These  Curves  show  Straight  Line  Relation 

between    ffv  and   -A=?  for  Constant  5 
Therefore  at  given  5 :-  9v**9  Q  ( 1  +    \/^ 


.5        1.0       1.5       2.0      2.5       3.0       3.5      4.0 

Yw 


FIG.  32. — Effect  of  temperature  on  the  strength  of  air.     X  measured  values. 


For  Concentric  Cylinders. 


0.308\    . 

7=^)  kv.  per  cm.  max. 


(25o) 


54 


DIELECTRIC  PHENOMENA 


For  Parallel  Wires. 


0.301\ 


gv  =  29.85  (1  H -7==-]  kv.  per  cm.  max. 

V  VSr  / 


(256) 


g70 

'eo 
I 

M*50 


30 


.9 


1.0 


1.1 


1.2        1.3 


FIG.  33. — Effect  of  temperature  on  the  strength  of  air.     (r  =  radius  of  wire 
in  cm.  X  measured  values.     Drawn  curves  calculated.) 

Referring  to  the  tables,  column  6  gives  values  of  gv  calculated 
from  equation  (25cc).  By  comparing  with  the  experimental 
values  in  column  5  it  is  seen  that  the  difference  is  generally  less 
than  1  per  cent. 


90 
80 

d  70 

r  GO 


50 


540 

53° 
20 

10 
0 


0    .1    .2    .3   .4    .5    .6     .7g.8    .9    1.01.11.21.31.4 

Fia.  34. — Effect  of  temperature  on  the  strength  of  air.     (  X  measured  values. 
Drawn  curves  calculated.) 

QO  has  a  slightly  higher  value  for  wires  in  a  concentric  cylinder 
than  for  parallel  wires.  This  does  not  mean  that  the  strength 
of  air  differs  in  the  two  cases.  For  a  wire  in  a  cylinder  the  field 
is  balanced  all  around  and  should  give  more  nearly  the  true  value. 


VISUAL  CORONA 


55 


In  Figs.  32,  33  and  34  the  drawn  lines  are  the  calculated  values, 
while  the  crosses  are  the  observed  values. 

Barometric  Pressure. — It  will  be  noted  in  Fig.  34  that  while  the 
calculated  curve  is  almost  a  straight  line  down  to  6  =  0.5,  below 
this  point  there  is  a  decided  bend  to  zero.  The  lower  part  of  this 
curve  was  drawn  from  calculations.  In  order  to  check  experimen- 
tally the  above  law  over  a  wide  range  of  5,  and  also  to  show  that  the 
effect  was  the  same  whether  the  change  was  made  by  varying  tem- 
perature or  pressure,  tests  were  made  over  a  large  pressure  range. 


Term! 


FIG.  35. — Apparatus  for  determining  the  effect  of  pressure  on  strength  of  air. 

A  glass  cylinder  lined  with  tin  foil  7.36  cm.  in  diameter  with  a  small 
slit  window  in  the  center  was  used  for  this  purpose.  (See  Fig.  35.) 
Tests  were  made  on  wires  0.508  cm.  to  0.157  cm.  in  diameter,  and 

TABLE  VIII. — VARIATION  OF  STRENGTH  OF  AIR  WITH  PRESSURE 

Diameter  of  Brass  Rod  =  0.381  cm.  in  7.36-cm.  Diameter  Glass 

Tube  Covered  with  Tin  Foil — 60  ~ 


Pres. 
abs. 
cm.  Hg 

Volts 
read 

(eff.) 

Temp, 
deg.  C. 

5  = 
3.926 

gv  - 
«» 

ff,,  max., 
measured 
kv./cm. 

gv  max.,  calculated 

/          0.301  x 
01  »(  -i   _i_  .  A 

r(log.R/r) 
kv./cm.  (eff.) 

old  V  1     i           —     I 

VSr  ' 

kv./cm. 

273  +  t 

5.3 

2,880 

27.0 

0.069 

5.08 

7.19 

7.80 

10.7 

4,580 

24.0 

0.141 

8.09 

11.45 

12.40 

11.2 

4,920 

27.0 

0.146 

8.68 

12.28 

12.15 

19.3 

7,400 

27.0 

0.252 

13.06 

18.47 

18.58 

27.7 

9,550 

27.0 

0.362 

16.87 

23.85 

24.06 

36.6 

12,000 

27.0 

0.478 

21.20 

30.00 

29.60 

46.4 

14,450 

25.0 

0.612 

25.50 

36.07 

35.70 

47.0 

14,600 

27.0 

0.614 

25.80 

36.50 

35.80 

55.7 

16,300 

27.0 

0.728 

28.80 

40.75 

40.75 

60.0 

17,760 

25.5 

0.792 

31.35 

44.30 

43.50 

66.0 

18,400 

27.0 

0.867 

32.50 

46.00 

46.75 

75.0 

21,100 

25.0 

0.997 

37.25 

52.70 

52.25 

56 


DIELECTRIC  PHENOMENA 


00 

50 
E  45 
S  49 
|35 

I  25 
|20 

5 

s^" 

Wire  Radius.-  .254  cm. 
o  =  Experimental  Values 
Drawn  Curve  -Calculated 

^ 

^ 

Values 

^ 

>^ 

r^~ 

>"• 

^ 

^ 

^ 

^ 

^ 

^^ 

^ 

^ 

*S 

-^ 

. 

^ 

X 

X 

0  .1  .        .2          .3  .4  -Bs.^-6          -7  '8          -9 

FIG.  36. — Effect  of  pressure  on  the  strength  of  air. 


ou 
55 
.  50 

s« 

JMO 
|35 
5  30 
*-25 
^20 

«515 
10 

5 

Wire  Eadius:.  .1905  cm. 
o  =  Expur-imwital  Values 
Drawu  Curve  -Calculated 

^ 

- 

^ 

** 

p-*^ 

^> 

^ 

^ 

^ 

-^ 

^ 

^^ 

^ 

*5 

X* 

^ 

S* 

x 

S 

/ 

.5, 


.92  6- 


1.0 


FIG.  37.  —  Effect  of  pressure  on  the  strength  of  air. 


ou 
55 

1  35 

r 

^20 

10 
5 

^ 

> 

— 

Wire  Radius  -.127  cm. 
o  a  Experimental  Va 
Drawn.  Curve  -  Calcula 

ues 

ed 

0 

^x- 

^ 

^ 

-^ 

x^ 

•^"^ 

. 

•X 

. 

X" 

S 

/ 

/ 

/ 

X 

. 

X 

/ 

-2          -3          .4          .53>926.6          .7 
5-   1J3?T 


.9          1.0 


FIG.  38. — Effect  of  pressure  on  the  strength  of  air. 


VISUAL  CORONA  57 

a  pressure  range  of  1.7  cm.  to  76  cm.  Table  VIII  is  typical 
of  observed  and  calculated  values.  Figs.  36,  37  and  38  show 
how  these  follow  the  previously  predicted  curve.  A  SA  reduction 
of  the  values  also  confirms  the  above  formulae.  For  concentric 
cylinders 

„.-   /,        0.308\ 

gv  =  olo(  1  H  --  /=r~)  max.  kv.  per  cm. 
\         vor  / 

For  parallel  wires 

gv  =  305(1  -\  —  '-7=-}  max.  kv.  per  cm. 
\  / 


The  change  in  gv  with  the  density  is  apparently  due  to  change  in 
the  molecular  spacing,  and  thus  depends  only  upon  the  relative 
density  and  not  the  absolute  density.  Heavy  CO2  at  the  same 
pressure  and  temperature  has  the  same  strength  as  air.  Corona 
in  hydrogen,  however,  appears  to  start  at  a  lower  voltage  than 
in  air. 

Electric  Strength  of  Air  Films.  —  If  a  definite  amount  of  energy 
is  necessary  to  start  rupture  at  a  finite  distance  a  from  the  con- 


,,-fl 

1  v^~\  *    i  /^N  v 

O  'MA 


FIG.  39. 

ductor,  with  a  surface  gradient  gv,  it  is  interesting  to  speculate 
what  will  happen  at  very  small  spacings  or  when  the  distance 
between  conductor  surfaces  is  in  the  order  of  a.  (See  Fig.  39.) l 

As  the  free  ''energy  storage,"  " accelerating"  or  "ionizing" 
distance  is  then  limited,  a  greater  force  or  gradient  should  be 
required  when  the  distance  between  the  conductors  approaches  a. 
Experiments  were  made  to  determine  this,  using  spheres  as  elec- 
trodes. The  ideal  electrodes  for  this  purpose  would  be  concentric 
cylinders,  but  the  use  of  these  as  well  as  parallel  wires  at  small 
spacing  seemed  impracticable.  Spark-over  and  corona  curves 
were  made  on  spheres  ranging  in  diameter  from  0.3  cm.  to  50  cm. 
and  spacings  from  0.0025  cm.  to  50  cm.  This  discussion  applies 
only  to  spacings  up  to  2R  where  corona  cannot  form. 

1  Actually,  the  "energy-zone"  is  not  as  shown,  as  the  field  is  distorted  at 
these  small  spacings. 


58 


DIELECTRIC  PHENOMENA 


In  these  tests  a  60-cycle  sine  wave  voltage  was  used.  For  the 
small  spacing  the  spheres  were  placed  in  a  very  rigid  stand.  One 
shank  was  threaded  with  a  fine  thread,  the  other  was  non-adjust- 
able (Fig.  40).  In  making  a  setting  the  adjustable  shank  was 
screwed  in  until  the  sphere  surfaces  just  touched,  as  indicated  by 
completing  the  circuit  of  an  electric  bell  and  single  cell  of  a  dry 
battery.  A  pointer  at  the  end  of  the  shank  was  then  locked  in 
place,  after  which  the  shank  was  screwed  out  any  given  number 
of  turns  or  fraction  of  turns  as  indicated  on  the  stationary  dial. 
For  larger  spacings  other  stands  were  used. 

A  typical  spark-over  spacing  curve  and  corona  spacing  curve 
is  shown  in  Fig.  41.  Theoretically,  up  to  a  spacing  of  2R  corona 
cannot  form  but  spark-over  must  be  the  first  evidence  of  stress. 

Practically,  corona  cannot  be  detected  at  60—  until  a  spacing 
of  SR  is  reached.  This  is  because  up  to  this  point  the  difference 


Pointer 


/-  Dial 
Stationary 


Wood 


FlG.    40. 

/  between  the  corona  starting  points  and  the  spark  point  is  very 
small.  Above  SR  the  spark-over  curve  approaches  a  straight  line 
as  in  the  case  of  the  needle  gap  curve.  The  corona  curve  above  2R 
and  the  spark  curve  below  2R  are  apparently  continuous.  The 
gradient  curve,  Fig.  42,  is  calculated  from  the  voltage  curve,  Fig. 
41.  Where  the  spacing  is  less  than  0.54\/R  the  gradient  increases 
first  slowly  and  then  very  rapidly  with  decreasing  spacing. 
Between  X  =  0.54V#  and  2R  the  gradient  is  very  nearly  con- 
stant. Above  about  3R  spacing  the  gradient  apparently  increases. 
This  apparent  increase  is  probably  due  to  the  effect  of  the  shanks, 
etc.,  which  become  greater  as  X  is  increased.  The  effect  of  the 
shanks  is  to  better  distribute  the  flux  on  the  sphere  surface,  and 
cannot  be  taken  account  of  in  the  equation  for  gradient.  This 
was  shown  experimentally  by  using  different  sizes  of  shanks  at 


VISUAL  CORONA 


59 


the  larger  spacing.  Thus,  when  the  spacing  is  greater  than  3R 
the  sphere  is  not  suitable  for  studying  the  strength  of  air,  as  the 
gradient  cannot  be  conveniently  calculated.  It  is  hence  not  a 
suitable  electrode  for  studying  corona,  as  corona  does  not  form 
until  the  spacing  is  greater  than  2R.  The  maximum  gradient  at 
the  surface  of  a  sphere  (non-grounded)  may  be  calculated  from 
the  equation.1 


-.54 


Spacing  -X- 


icing  -X- 


FIG.  41. — Variation  of  corona  and  spark-    FIG.  42. — Variation  of  strength 
over  voltages  with  spacing  for  spheres.  of  air  with  spacing  for  spheres. 


(13o) 


where   X  is  the  spacing 
E  the  voltage 


The  gradient  for  the  non-grounded  case  may  be  conveniently 
calculated  by  use  of  the  table  on  page  27.  The  gradient  on  the 
line  connecting  the  sphere  centers  at  any  distance  a  from  the 
sphere  surface  may  be  calculated  from  the  complicated  equation2 


|  -  a)  \f  -  1)] 


(26) 


Some  of  the  experimental  values  are  given  in  Tables  IX  and  X. 
Typical  voltage  gradient  curves  are  shown  in  Figs.  43,  44  and  45. 

1  G.  R.  Dean,  G.  E.  Review,  March,  1913. 

2  G.  R.  Dean,  also  Physical  Review,  Dec.,  1912,  April,  1913. 


60 


DIELECTRIC  PHENOMENA 


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Spacing  in  cms. 

Fig.  45. 

^ 

\ 

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Xj 

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^ 

X 

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^ 

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VISUAL  CORONA 


61 


TABLE  IX. — SPARK-OVER  OF  SPHERES  AT  SMALL  SPACINGS 
Brass  Spheres  R  =  3.33  cm.,  Diameter  =  2-5/8  in. — 60  ~ 


X              Spacing 

feff- 

Kv. 

3 
3.926 

* 

V2  (eeff.) 

Qmax. 
emox-  , 

X/R 

In. 

Cm. 

s 

(corrected) 

=     X   f 

kv./cm. 

273  +  t 

0.001 

0.00254 

0.363 

1.028 

0.497 

196.0 

0.00076 

0.002 

0.00508 

0.531 

1.030 

0.729 

143.6 

0.00152 

0.003 

0.00762 

0.654 

1.027 

0.899 

118.1 

0.00228 

0.004 

0.01016 

0.775 

1.026 

1.07 

105.2 

0.00305 

0.005 

0.0127 

0.845 

1.016 

1.17 

92.3 

0.00382 

0.010 

0.0254 

1.07 

1.000 

1.52 

60.0 

0.00764 

0.020 

0.0508 

1.86 

1.002 

2.62 

51.8 

0.01528 

0.040 

0.1016 

3.27 

1.002 

4.62 

45.9 

0.03056 

0.075 

0.1905 

5.43 

1.002 

7.66 

41.0 

0.05730 

0.100 

0.254 

6.92 

1.002 

9.77 

39.5 

0.0764 

0.200 

0.508 

12.40 

1.002 

17.50 

36.3 

0.1528 

0.300 

0.762 

17.70 

1.002 

25.00 

35.4 

0.2292 

0.400 

1.016 

22.70 

1.002 

32.00 

34.8 

0.3056 

0.500 

1.270 

27.75 

1.002 

39.20 

34.9 

0.382 

TABLE  X. — SPARK-OVER  OP  SPHERES  AT  SMALL  SPACINGS 
Brass  Spheres  R  =  12.5  cm.,  Diameter  =  9.84  in. — 60  ~ 


X                Spacing 

€eff. 

Kv.    (read) 

5 
3.92b 

_\/2(ee//.) 

Omax. 
_ejna, 
~     X     ' 

kv./cm. 

X/R 

In. 

Cm. 

273+f 

a 

(corrected) 

0.005 

0.0127 

0.807 

1.023 

1.116 

87.9 

0.00101 

0.010 

0.0254 

1.220 

1.021 

1.689 

66.5 

0.00203 

0.020 

0.0508 

2.050 

1.031 

2.849 

55.9 

0.00406 

0.040 

0.1016 

3.38 

1.022 

4.68 

46.2 

0.00813 

0.100 

0.254 

7.03 

1.020 

9.75 

38.6 

0.0203 

0.200 

0.508 

12.54 

1.012 

17.44 

34.8 

0.0406 

0.300 

0.762 

17.91 

1.016 

24.92 

33.5 

0.0609 

0.400 

1.016 

22.82 

1.010 

31.76 

32.0 

0.0812 

0.500 

1.27 

27.63 

1.010 

38.67 

31.5 

0.1016 

1.000 

2.54 

53.0 

1.000 

74.90 

31.6 

0.2032 

1.500 

3.81 

75.3 

1.000 

106.30 

30.9 

0.3048 

2.000 

5.08 

96.4 

l.OOQ 

136.20 

30.5 

0.4064 

2.500 

6.35 

117.4 

1.000 

166.00 

30.7 

0.5080 

3.000 

7.62 

139.2 

1.000 

196.90 

31.2 

0.6096 

3.500 

8.89 

158.0 

1.000 

223.40 

31.3 

0.7112 

4.000 

10.16 

174.9 

1.000 

247  .  10 

31.0 

0.8128 

4.500 

11.43 

190.8 

1.000 

269.50 

31.0 

0.9144 

5.000 

12.70 

203.6 

1.000 

287.20 

30.8 

1.0160 

*  At  low  air  density  and  small  spacings  correction  must  be  made  by 
Paschen's  Law.     See  page  196.     Also  appendix. 


62 


DIELECTRIC  PHENOMENA 


In  Table  XI  are  tabulated,  for  different  sizes  of  spheres,  the 
spark-over  gradient  at  the  constant  part  of  the  curve,  the  aver- 
age gradient  between  X  =  0.54  V-R  and  X  =  3R,  and  the  approxi- 
mate minimum  spacing  at  which  the  gradient  begins  to  increase 

TABLE  XI. — MAXIMUM  RUPTURING  GRADIENTS  FOR  SPHERES 
(Average  for  Constant  Part  of  the  Curve) 


R 

Radius  in  crn. 

Spacing  X,  where  gs  begins 
to  increase  (cm.) 

gs  max.  kv./cm.  for  constant 
part  of  curve 

0.159 

0.18 

63.8 

0.238 

0.25 

55.6 

0.356 

0.26 

51.4 

0.555 

0.40 

46.9 

1.270 

0.51 

40.0 

2.540 

0.85 

36.8 

3.120 

35.8 

3.330 

0.95 

34.8 

6.25 

1.30 

32.5 

12.50 

2.0 

31.3 

25.00 

30.0 

65  E  — 

2   5|  \ 

o40 
•2«L 

'X 

^ 

s35! 

1  — 

—  

-o  , 



=j 

n'30| 

c:        1 

3  251 

*j      1 
a  r>nl 

i^L 

&15I 

°mU 

"0     1     2     3    4     5     6     7     8     9    10   11  12   K 
Radius  in  cms. 

FIG.  46. — Variation  of  the  apparent  strength  of  air  with  sphere  radius. 
Points  measured  gradient  from  constant  part  of  curve.  Drawn  curve, 
calculated  from  equation  (27). 

in  value.     The  gradient-radius  curve  is  plotted  in  Fig.  46.     This 
curve  is  very  closely  given  by  the  equation 


,.  --  ,(: 


(27) 


VISUAL  CORONA 


63 


which  has  exactly  the  same  form  as  the  similar  curve  for  cylinders. 
The  value  of  g0  is,  however,  lower  than  for  the  balanced  field  of  a 
wire  in  a  cylinder. 

0.308X 


For  a  wire  in  a  cylinder    g0  =  31 


For  parallel  wires 


For  spheres 


g0  =  30       gv  = 


=  27.2    gv  = 


(25a) 
(256) 
(28) 


*• 

g*»v 

^ 

^ 

0.1.8 

CO  1    /• 

s* 

^ 

a1'6 

|1.4 

|L2 

x 

^ 

/ 

^ 

/ 

s  i.o 

I   .8 

?  .1 

K  .2 

0 

X 

4 

/ 

/ 
' 

o 

It  is  probable  that  the  true  strength  of  air  is  31  kv.  per  centimeter 
as  represented  by  the  balanced  field,  it  is  apparently  less  for  parallel 
wires  due  to  the  unbalanced  field,  and  still  less  for  spheres  where 
the  field  is  unbalanced  to  a 
greater  extent. 

The  curve  between  the 
sphere  radius  and  the  ap- 
proximate minimum  spacing 
below  which  the  gradient  be- 
gins to  increase  appreciably 
is  plotted  in  Fig.  47  from 
Table  XI.  The  curve  is  rep- 
resented by  the  equation 

X  =  0.54VS         (29) 

which  means  that  when  the 

spacing  is  less  than  0.54  \/R  the  gradient  increases  in  value,  at 

first  slowly,  then  very  rapidly. 

It  is  now  interesting  to  investigate  the  meaning  of  equation 
(27).  In  Fig.  48  the  exact  gradient  is  plotted  from  equation  (26) 
for  different  distances  from  the  sphere  surface  on  the  line  con- 
necting the  centers  and  at  given  spacings  as  indicated  by  the  small 
diagram  in  the  upper  corner  of  the  figure.  It  is  seen  that  for 
small  distances  from  the  sphere  surface  the  curves  for  the  differ- 
ent spacings  fall  together.  Over  the  small  range  the  gradient 
ga  at  any  point  a  centimeters  from  the  sphere  surface  on  the 
center  line  may  be  found  approximately  from 


12345 

Radius  in  Centimeters 

FIG.  47. — Sphere  spacing  below  which 
apparent  strength  begins  to  increase. 


(30) 


The  only  reason  for  giving  this  approximation,  which  holds 
only  for  very  small  values  of  a  and  is  only  true  when  a  =  0,  is 


64 


DIELECTRIC  PHENOMENA 


that  (26)  is  too  complicated  to  handle.     The  error  due  to  this 
approximation  is  shown  in  Table  XII. 


TABLE  XII 


R  =  1.27  cm. 
Energy  distance,  a  =  0.27  \/R  =  0.3  cm. 

R  =  12.5  cm. 
Energy  distance,  a  =  0.95  cm. 

a 

0  a, 

Exact 

Qa, 

Approx. 

X 

a 

Qa, 

Exact 

A     °a' 

Approx. 

X 

0.0 

39.9 

39.9 

0.76 

0.0 

31.3 

31.3 

4 

0.1 

34.6 

34.0 

0.76 

0.2 

30.3 

30.3 

4 

0.2 

31.9 

30.0 

0.76 

0.4 

29.5 

29.4 

4 

0.4 

29.7 

24.1 

0.76 

0.6 

28.6 

28.5 

4 

0.8 

28.3 

27.7 

4 

0.0 

39.9 

39.9 

1.21 

1.0 

27.5 

26.9 

4 

0.1 

34.2 

33.4 

1.21 

0.2 

30.5 

29.5 

1.21 

0.0 

31.3 

31.3 

10 

0.4 

26.5 

23.7 

1.21 

0.2 

30.3 

30.3 

10 

0.4 

29.5 

29.4 

10 

0.6 

28.6 

28.7 

10 

0.8 

28.0 

27.7 

10 

1.0 

27.5 

26.9 

10 

Then 


ga  =  VjJf  =  ;|(!/)  exact 


mathematical. 


\  experimental  for  approximately 
constant  part  of  curve. 


—  f]  approximate  mathematical. 
Equating  (I3a)  and  (27) 


(13a) 


(30) 


which  is  the  same  form  as  (30)  and  means  that  at  a  distance 


from  the  sphere  surface  the  gradient  at  rupture  is  always  approxi- 
mately constant  and  is  g0._  As  breakdown  must  take  place  at 
approximately  a  =  0.27  V^  cm.  from  the  sphere  surface,  the 


VISUAL  CORONA 


65 


gradient  should  begin  to  increase  at  the  spacing  2a  =  0.54 \/R. 
This  is  approximately  so  as  shown  in  Fig.  47  and  equation  (30). 
The  increase  is  at  first  slow  at  X  =  2a,  and  very  rapid  at  X  =  a. 
Fig.  48  shows  that  at  a  =  0.27\/R  the  gradient  is  not  exactly 
constant  for  different  spacings,  or  the  curves  do  not  fall  together. 


•0 
34 
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£30 

|28 
|26 
M24 
122 
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S18 

I16 

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«ll2 

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Jalc 

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tior 

of  JGra 

diei 

it 

/ 

bet 

veu 

18 

she 

•es 

' 

\ 

/ 

\ 

U 

=  1 

cm. 

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s% 

V 

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#  = 

'2   C 

n. 

^ 

<- 

-0- 

3 

T 

^ 

t 

^ 

5 

— 

j_.. 

¥ 

^ 

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—  £ 

=  4 

cm 

3a 

12., 

=  ( 

2 

Cl 

Jradieut  on  Line 
AB  at  Distance 
rom  Surface  of  Sj 
n.  Spheres 

^ 

^x 

)here 

^^ 

^ 

t^ 

"^ 

^ 

^^ 

^, 

X 

=10 

cm 

^^ 

<; 

•^ 

•^-^^^ 

-». 

^ 

<: 

X" 

15  cm. 

33 

^  —  . 

x=~o  cm. 

a 

Distance  from  Surface  of  Sphere 

FIG.  48. — Gradient  at  different  points  on  line  through  centers  of  spheres. 
Calculated  from  (26). 

This  means  that  g0  and  °c  in  equation  (27)  cannot  be  exactly 
constant  for  a  given  radius,  but  must  also  be  a  function  of  X. 
This  is  experimentally  shown  to  be  the  case,  as  there  is  a  slight 
variation  over  the  range  X  =  0.54\/jR  and  X  =  2R. 
Influence  of  Frequency  on  the  Visual  Gradient. — The  effect 


40 


0    100   200  300   400   500   600   700   800   900  1000 
Frequency  Cycles/Sec. 

FIG.  49. — Variation  of  the  apparent  strength  of  air  with  frequency. 

of  frequency  on  gv  for  the  practical  range  of  25  to  60  cycles,  if 
any,  is  very  small  and  can  be  neglected.  A  few  measurements  are 
shown  in  Fig.  49.  For  the  test  range  it  is  difficult  to  tell  whether 
the  slight  variations  are  due  to  changes  in  wave  shape  or  to  fre- 


66 


DIELECTRIC  PHENOMENA 


quency.     There  is  a  possibility  of  frequency  entering  this  as  a 
function : 


\ 


Investigations  up  to  1000  cycles  show  very  little  if  any  change. 
In  this  investigation  the  sine  wave  voltage  was  measured  with  a 
static  voltmeter  calibrated  at  60  cycles.  Measurement  at  30,000 
cycles  (sine  wave  from  a  generator)  made  by  the  static  volt- 
meter showed  a  slightly  lower  voltage  than  at  60  cycles.1  Direct 
current  points  by  Watson  are  given  in  Fig.  49.  See  appendix. 
Over  the  commercial  range  of  frequency,  however,  there  is  no 
appreciable  effect  of  frequency.  For  transient  corona  see  page 
108  and  appendix. 

Effect  of  Oil,  Water  orDirt  on  the  Visual  Corona  Point.— These 
tests  were  made  in  a  manner  exactly  similar  to  the  dry  tests. 


10      20     30     40      50     60       70  0      10      20      30     40      50      60      70 

Spaciug.in  cms.   Between  Centers  Spacing  in  cms.    Between  Centers 

FIGS.  50  and  51. — Spark-over  and  corona  voltages  for  parallel  wires. 
(Wire  surfaces  dry,  wet,  and  oiled.  Max.  kv  to  neutral.  8  =  1.  Fig.  50. — 
Wire  radius  0 . 205  cm.  Fig.  51.— Wire  radius  0 . 129  cm.) 

In  the  oil  tests,  the  surface  of  the  wire  was  coated  with  a  thin, 
even  film  by  means  of  an  oiled  cloth.  For  the  wet  tests  water 
was  sprayed  on  the  conductor  surface  before  each  reading  by 
means  of  an  atomizer.  Figs.  50  and  51  are  dry,  wet  and  oil 
curves  for  two  different  sizes  of  wire. 

For  spark-over,  both  water  and  oil  have  approximately  the 
same  effect,  that  is,  give  very  nearly  the  same  spark-over  voltage 
for  all  sizes  of  conductor.  The  curves  very  closely  follow  the 
needle  gap  curve. 

For  corona,  water  very  greatly  lowers  gv.     Oil  lowers  gv  but  to  a 

1  See  pages  106,  107, 


VISUAL  CORONA 


67 


much  less  extent  than  water.  When  the  conductor  is  very  small 
the  per  cent,  increase  in  diameter  due  to  oil  more  than  com- 
pensates for  the  lowering  effect.  The  approximate  apparent 
visual  corona  gradient  for  oil  and  water  coated  conductors  may 
be  found 
Water  surfaces  by  fine  spray  or  fog 

gv  =  9{  1  H  —  '—7=-}  max.  kv.  per  cm. 
\  V  r  ) 

Oil  film  surfaces 

gv  =  19(  1 
\ 


'      )  max.  kv.  per  cm. 
Vr 


See  Fig.  52. 

If  a  water  coated  wire  above  the  visual  corona  point  is  exam- 
ined in  the  dark,  it  has  the  appearance  of  an  illuminated  atomizer. 
The  surface  quickly  becomes  dry. 


030 


MM 

• 


£]•*>•    tooootM-^eooooN-^toooo 

•   •    •   '33333«i«i«i<*!0t«i 
FIG.  52. — Apparent  strength  of  air  around  wires  with  wet  and  oiled  surfaces. 

Dirt  on  the  surface  of  the  conductor,  by  increasing  the  gradient, 
causes  local  brush  discharges,  and  if  the  surface  is  rough,  corona 
starts  at  a  lower  voltage.  This  is  taken  care  of  in  the  formulae 
by  an  irregularity  factor  mv.  Thus  for  a  weathered  or  oxidized 
wire 

0.301  \ 


The  corona  starting  voltage  for  wet  or  oiled  wires  may  be 
found  by  calculating  gv  in  the  above  equations  and  substituting 
in  equation  (20). 


68 


DIELECTRIC  PHENOMENA 


Conductor  Material. — With  the  same  surface  condition  the 
visual  corona  point  is  independent  of  the  material.  This  is  shown 
in  Table  II. 

Humidity. — Tests  made  over  a  very  wide  humidity  range  show 
that  humidity  has  no  appreciable  affect  upon  the  starting  point 
of  visual  corona.  After  corona  is  present  humidity  has  an  effect 
on  the  spark-over  voltage.  This  is  discussed  in  Chapter  IV. 

lonization. — Change  of  initial  ionization  of  the  air  even  to  a 
considerable  extent  has  no  appreciable  effect  on  the  starting  point 
of  corona.  This  was  found  by  test  by  increasing  the  voltage 
on  the  wire  in  the  cylinder  until  considerably  above  the  corona 
voltage,  and  then,  while  the  cylinder  was  full  of  ionized  air,  lower- 
ing the  voltage  below  the  corona  point  and  again  raising  it  until 
glow  appeared.  The  starting  point  was  not  appreciably  changed. 
Initial  ionization  should,  however,  effect  the  time  in  which  the 
discharge  takes  place.  This  will  be  discussed  later. 

Current  in  Wire. — A  test  was  made  to  see  if  heavy  currents 
flowing  in  the  wire  would  change  the  starting  point  of  visual 
corona.  The  test  arrangement  was  as  shown  in  the  Fig.  53. 


May  be  Cor 
in  Either 


FIG.  53. — Apparatus  for  measuring  corona  starting  point  with  current  in 

the  wires. 


Tests  were  made  with  both  a.c.  in  phase  and  out  of  phase,  and 
d.c.  in  the  wire.  The  results  are  given  in  Tables  XIII,  XIV  and 
XV.  The  temperature  of  the  wire  was  measured  by  the  resist- 
ance method.  The  values  in  the  last  column  are  all  corrected 
from  the  wire  temperature  to  5  =  1.  If  the  current  has  no 
appreciable  effect,  as  appears  to  be  the  case,  these  should  all  be 
equal.  The  variation  is  probably  due  to  difficulty  in  getting  the 


VISUAL  CORONA 


69 


TABLE  XIII. — CORONA  STARTING  POINT  WITH  CURRENT  FLOWING  THROUGH 

WIRE 
Concentric  Cylinders 

Radius  of  wire 0. 129  cm. 

Radius  of  cylinder 5.46  cm. 


Kv.   eff. 

Amp. 
d.c. 

Average 
temperature 

Barom.  cm. 

5  (using 
wire  temp.) 

0V 

gv  reduced 
to  5  =  1 

Air 

Wire 

20.0 
19.7 
19.4 
18.5 
17.8 
16.9 
20.4 
20.3 
19.4 
17.9 
12.9 
16.4 
13.9 
16.1 

0.0 
15.2 
31.4 
39.0 
49.2 
75.0 
0.0 
18.0 
33.0 
50.8 
99.6 
67.6 
78.6 
61.6 

26 
26 
26 
26 
26 
26 
23 
23 
23 
24 
24 
26 
26 
26 

26 
32 
48 
64 
82 
120 
23 
27 
50 
91 
320 
102 
212 
144 

75.6 

0.991 
0.970 
0.922 
0.878 
0.824 
0.753 
1.000 
0.987 
0.917 
0.813 
0.500 
0.790 
0.610 
0.710 

58.4 
57.5 
56.7 
54.1 
52.0 
49.4 
59.6 
59.3 
56.7 
52.2 
37.6 
47.9 
40.8 
47.0 

58.9 
59.2 
61.4 
61.6 
63.1 
65.6 
59.6 
59.9 
61.8 
64.2 
75.2 
60.6 
67.0 
66.2 



TABLE  XIV. — CORONA  STARTING  POINT  WITH  CURRENT  FLOWING   THROUGH 

WIRE 
Concentric  Cylinders 

Radius  of  wire .  0 . 205  cm. 

Radius  of  cylinder 5.46    cm. 


Kv.   eff. 

Amp. 

Average 
temperature 

Barom.  cm. 

5    (using 
wire  temp.) 

ff» 

gv  reduced 
to  5  =   1 

Air 

Wire 

25.3 

14  (d.c.) 

23 

23 

76.2 

1.01 

53.15 

52.6 

25.2 

0 

23 

23 

76.2 

1.01 

53.0 

52.5 

25.2 

14  (a.c. 

23 

23 

75.8 

1.005 

52.8 

52.6 

in  phase) 

25.1 

14  (a.c. 

23 

23 

75.8 

1.005 

52.6 

52.3 

out  of  phase) 

25.1 

0 

23 

23 

75.8 

1.005 

52.6 

52.3 

25.2 

0 

24 

24 

75.25 

0.994 

52.8 

53.2 

25.2 

14  (d.c.) 

24 

30 

75.25 

0.974 

52.8 

54.3 

25.2 

34  (d.c.) 

25 

60 

75.25 

0.886 

52.4 

59.1 

23.8 

56  (d.c.) 

29 

60 

75.25 

0.886 

50.0 

56.3 

23.3 

70  (d.c.) 

30 

73 

75.25 

0.853 

48.8 

57.3 

21.8 

114  (d.c.) 

110 

75.25 

0.771 

45.7 

59.2 

25.0 

60  (d.c.) 

31 

31 

75.25 

0.971 

52.4 

53.9 

25.0 

0 

31 

31 

75.25 

0.971 

52.4 

53.9 

24.8 

23  (a.c.) 

31 

44 

75.25 

0.931 

52.0 

55.8 

70 


DIELECTRIC  PHENOMENA 


TABLE  XV. — CORONA  STARTING  POINT  WITH  CURRENT  FLOWING  THROUGH 

WIRE 

Concentric  Cylinders 

Radius  of  wire 0.476  cm. 

Radius  of  cylinder 5.465  cm. 


Average 

Kv.  eff. 

Amp.  d.c. 

temperature 

Barom.  cm. 

5  (using 

Qv 

QV  reduced 
to  6  —  1 

Air 

Wire 

36.5 

0 

27 

27 

75.5 

0.985 

44.3 

45 

36.5 

80 

27 

27 

75.5 

0.985 

44.3 

45 

'exact  temperature  of  the  air.  The  air  immediately  surrounding 
the  wire  is  assumed  to  be  at  the  same  temperature  as  the  wire. 
This  causes  a  correction  that  is  too  large.  Current  flowing  in  a 
wire  thus  probably  does  not  appreciably  effect  the  corona  point 
unless  the  temperature  of  the  wire  is  increased. 

Stranded  Conductors  or  Cables. — While  the  visual  critical 
corona  point  is  quite  sharp  and  definite  for  wires,  it  is  not  so  for 


50 


.6  .8  1.0 

Diameter  in  cms. 


FIG.  54. — Apparent  visual  critical  corona  voltages  for  parallel  cables. 
Numerals  denote  number  of  strands:  I,  polished  copper  wire;  II,  decided 
corona  on  cable,  o;  III,  local  corona  all  along  cable,  x. 

cables  or  standard  conductors.  Corona,  after  it  first  appears, 
increases  gradually  for  a  considerable  range  of  voltage  until  a 
certain  definite  voltage  is  reached  where  the  increase  is  very  rapid. 
The  first  point  has  been  called  the  local  corona  point,  and  the 
second  point  the  decided  corona  point.  The  curve,  Fig.  54,  for 
these  corona  points  is  compared  with  the  curve  for  a  smooth 


VISUAL  CORONA 


71 


conductor.     The  starting  point  for  cables  may  be  found  by  the 
use  of  an  irregularity  factor,  mv. 

/i        0.301X, 

gv  =  g0mv[  1  H -T=-  }  kv.  per  cm. 

V  V  r  I 

where   mv  =  .82  for  decided  corona 
mv  —  .72  for  local  corona 
r    =  overall  radius  of  cable. 

This  applies  to  cables  of  six  strands  or  over. 

It  is  interesting  to  note  that  for  the  decided  corona  point  the 
visual  critical  voltage  of  a  cable  is  about  3  per  cent,  lower  than 
that  of  a  wire  with  the  same  cross-section,  or,  more  exactly  "the 
diameter  of  a  solid  wire  with  the  same  critical  voltage  is  about  97 
per  cent,  that  of  the  wire  having  the  same  cross-section  as  the 
cable."1  This  is  shown  in  Table  XVI. 

TABLE  XVI. — EFFECT  OF  STRANDING 
Whitehead,  A.I.E.E,  June,  1911,  Table  III 


Cables, 

Diameter 

Diameter  solid 

Diameter  solid 

Pitch  of  spiral 

strands 
outer 

over 
all 

of  equal 
section 

of  equal  crit- 
ical volts 

C/B 

C/A 

layer 

(A) 

(B) 

(CO 

Cm. 

Diameters 

3 

0.349 

0.272 

0.247 

0.907 

0.708 

3.81 

10.9 

4 

0.404 

0.332 

0.320 

0.965 

0.792 

3.49 

8.6 

5 

0.45 

0.381 

0.370 

0.971 

0.822 

4.44 

9.9 

6 

0.49 

0.430 

0.420 

0.975 

0.857 

6.02 

12.3 

7 

0.541 

0.480 

0.465 

0.969 

0.868 

6.66 

12.3 

8 

0.589 

0.530 

0.516 

0.975 

0.877 

6.35 

10.8 

9 

0.64 

0.581 

0.567 

0.977 

0.886 

6.98 

10.9 

3 

0.336 

0.27 

0.307 

0.767 

0.616 

None 

None 

4 

0.378 

0.312 

0.25 

0.802 

0.665 

None 

None 

N/ 


Conductors  of  the  Same  Potential  Close  Together. — When 
conductors  of  the  same  potential  are  arranged  close  together  the 
critical  breakdown  voltage  is  much  greater  than  that  of  a  single 
conductor  or  when  they  are  far  apart.  The  simplest  case,  that  of 
two,  is  shown  in  Fig.  55.  The  two  conductors  for  a  given  test 
were  kept  at  a  constant  distance  S/2  from  the  ground  plate. 
Potential  was  applied  between  the  conductors  and  plate.  The 
separation  m  was  then  varied  and  critical  voltages  read  at  differ- 

1  Whitehead,  Dielectric  Strength  of  Air,  A.I.E.E.,  June,  1911. 


72 


DIELECTRIC  PHENOMENA 


ent  spacings.  Refer  to  Fig.  56  (0.163-cm.  wire  30  cm.  from  neutral 
plane).  When  m  =  0,  ev  =  31.5  eff.  As  the  spacing  m  was  in- 
creased, ev  increased  to  a  maximum  of  35.8  kv.  With  increasing 
ev  then  gradually  decreases  to  a  constant  value  which  is  the 


m 


same  as  that  for  a  single  wire.     The  maximum  voltage  is  about  5 


40 


M 

T2 

L 


Ground  Plate 


10 


r 

6. 


gle 


0       5      10    15     20    25    30    35     40    45    50 

Separation  -m  -  cm. 

FIG.  55. — Arrangement  for  two  FIG.  56. — Critical  voltage  on  two 
conductors  at  same  potential,  and  conductors  at  the  same  potential  and 
plate.  various  separations  (see  Fig.  55). 

per  cent,  greater  than  the  critical  voltage  of  a  single  conductor  of 
the  same  cross  section. 

With  the  same  amount  of  conductor  material,  much  higher 
voltages  can  be  used  without  corona  loss  when  the  conductor  is 


pnnnnnnn 


0       5     10    15     20    25     30    35    40     45    -50    55    60 
Spacing-  S-cm. 


FIG.  57. — Conductors  of  the    FIG.    58. — Critical  voltages  for  conductors 
same  potential  arranged  in  a  arranged  as  in  Fig.  57. 

triangle. 

split  up  into  three  or  more  small  conductors,  properly  arranged, 
than  with  a  single  conductor.  The  results  of  tests  made  on  a 
single-phase  line  with  split  conductors  arranged  in  a  triangle 
as  in  Fig.  57  are  given  in  Fig.  58.  Fig.  58  shows  curves  for  a 
single  split  wire  and  also  for  a  single  wire  of  a  cross  section  equal 


VISUAL  CORONA 


73 


to  that  of  the  three  split  conductors.  Fig.  59  shows  how  the 
voltage  varies  with  varying  m. 

With  the  split  conductor  arrangement,  in  the  special  case  given, 
the  critical  voltage  is  from  20  to  30  per  cent,  greater  than  that  of  a 
single  wire  containing  the  same  amount  of  material. 

Whitehead  has  made  similar  tests  on  three  wires  in  a  triangle 
and  also  four  wires  placed  on  a  square  in  the  center  of  a  cylinder. 


Critical  Voltage  -Q  v  -  KV 
g  g  §  §  1  £ 

f\ 

\ 

\ 

Equi 
V 

ralent 
'ire 

S 

iigle 

Vire 

0         5        10        15       20       25       30       35       40        45       50 
Separatiou  Tfl>   Cm 

FIG.  59. — Critical  voltage  of  conductors  arranged  as  in  Fig.   57.     (S  = 
constant  =  40  cm.,  m  varying.) 

He  finds  16  per  cent,  increase  for  three  wires  and  20  per  cent, 
for  four  over  the  critical  voltage  of  a  single  conductor  of  the  same 
total  material. 

STROBOSCOPIC  AND  PHOTOGRAPHIC  STUDY 

Photographic  Study. — A  photographic  study  of  corona  on  wires 
and  cables  was  made  as  follows:  Two  parallel  conductors  were 
spaced  122  cm.  between  centers.  The  camera  was  focused 
on  one  conductor  only.  The  distance  to  the  lens  was  such 
as  to  show  the  conductors  at  approximately  actual  size.  An 
exposure  was  made  for  a  given  time  at  a  given  voltage. 
The  plate  was  then  shifted  slightly,  the  voltage  increased 
and  a  second  exposure  was  made  for  the  same  time.  That 
is,  a  given  series  shows  the  same  part  of  the  same  single  wire 
at  different  voltages.  This  operation  was  repeated  until  the 
series  for  a  given  wire  was  complete.  A  glass  lens  was  used  unless 
otherwise  stated.  (See  Fig.  60.)  These  photographs  are  shown 
in  Figs.  61  to  68. 

Photographs  67  and  68  were  made  to  show  the  effects  of  mois- 
ture. In  Fig.  67  the  stranded  cable  was  brought  up  to  the  critical 
point.  Water  was  then  thrown  on  the  cable.  The  result  is 
shown  in  Fig.  68.  What  was  a  glow  at  the  surface  of  the  dry 


74 


DIELECTRIC  PHENOMENA 


cable  became  at  the  wet  spots,  a  discharge  extending  from  5  to  8 
cm.  from  the  conductor  surface.  The  discharge  has  the  appear- 
ance of  an  illuminated  atomizer. 

Diameter  of  Corona. — On  a  smooth  wire  the  boundary  line  of 
corona  appears  to  be  fairly  definite.  The  apparent  visual  diame- 
ter may  be  measured  by  viewing  through  a  slit.  The  apparent 
diameter  may  also  be  found  photographically.  If  the  photo- 
graph is  made  through  a  quartz  lens  the  ultraviolet  rays  will 
not  be  cut  off  from  the  plates  as  when  a  glass  lens  is  used. 

Whitehead  has  made  some  measurements  on  the  apparent  diame- 
ter, comparing  the  visual  method  and  the  photographic  method 
with  both  quartz  and  glass  lenses.  He  finds  that  the  apparent 
diameters  are  respectively  by  the  visual,  glass  lens,  and  quartz 
lens  methods  in  the  ratios  of  1  :  1.6  :  1.9. l  It  therefore  appears 
that  there  is  a  considerable  content  of  the  corona  at  the  ultra- 
violet which  is  not  visible  to  the  eye.  As  soon  as  corona  appears 
it  seems  to  have  a  definite  finite  thickness. 


Plate  Direction' of  Shift 

FIG.  60. — Method  of  making  corona  photographs. 

TABLE  XVII. — DIAMETER  OF  CORONA  ON  WIRE  IN  THE  CENTER    OP  A 

CYLINDER 

Diameter  wire  0.233  cm.,  18.6-cm.  cylinder 
Fig.  9  (Whitehead,  A.I.E.E.,  June,  1912) 


Kilovolts 

Diameter  corona, 

Time, 

Lens 

No. 

Diameter  corona, 
visual    method, 

mm. 

mm. 

mm. 

22.5 

5.5 

2 

Glass 

(a) 

27.5 

9.3 

2 

Glass 

(b) 

32.5 

11.1 

2 

Glass 

(c) 

6.7 

1  Whitehead,  Electric  Strength  of  Air,  A.I.E.E.,  June,  1912. 


FIG.    61. — Corona   on  bright    tinned    phosphor-bronze    wire.      Diameter, 

A     AK1     ,», 


0.051  cm. 


FIG.  62. — Corona  on  copper  wire  polished  after  each  exposure.      Diameter. 

0.186  cm. 

(Facing  page  74.) 


FIG.  63. — Corona  on  a  polished  copper  wire.    Diameter,  0 . 186  cm.     Oper- 
ated at  200  kv.,  then  allowed  to  stand  idle.      (This  shows  effect  of  oxidation.) 


FIG.  64. — Corona  on  a  weathered  galvanized  iron  wire.     Diameter,  168  cm. 


3/o    Copper  Cable    Diam      U8Cm 


ZOO    kv 


FIG.  65. — Corona  on  a  1.25  cm.  polished  brass  rod  and  unpolished  copper 

cable. 


FIG.  66. — Corona  on  a  No.  3/0  weathered  cable. 

(Following  Fig.  64.) 


FIG.  67. — Corona  on  a  No.  3/0  line  cable.     Dry. 


FIG.  68. — Corona  on  a  No.  3/0  line  cable.     Wet. 

(Facing  page  75.) 


VISUAL  CORONA 


75 


TABLE  XVIII. — DIAMETER  OF  CORONA,  WITH  AND  WITHOUT  ULTRAVIOLET 

CONTENT 

(On  a  Wire  in  the  Center  of  a  Cylinder) 

Exposure  20  min.,  32.5-kv.  cylinder,  diam.   =   18.6  cm. 

(Whitehead,  A.I.E.E.,  June,  1912) 


0.232-cm.  wire 

0.316-cm.  wire 

0.399-cm.  wire 

Quartz 
and  glass 

Quartz 
alone 

Quartz 
and  glass 

Quartz 
alone 

Quartz 
and  glass 

Quartz 
alone 

12.0 

12.4 

12.5 

13.3 

11.4 

13.0 

11.5 

12.6 

13.0 

14.0 

11.6 

13.0 

11.5 

12.6 

13.0 

14.0 

12.0 

12.8 

11.4 

13.0 

12.8 

14.0 

12.0 

12.8 

11.6 

12.6 

12.8 

13.8 

11.7 

12.9 

Figs.  69,  70  and  71  and  Tables  XVII  and  XVIII  taken  from 
Whitehead  are  self  explanatory.  Fig.  721  shows  the  apparent 
diameter  of  corona  on  a  given  wire.  At  the  start  the  corona 


1.4 

a1-2 

i 

*  1.0 
I  0.8 

I  °-6 
I  0.4 


0.2 


1.4 

a1'2 

I  1.0 
Jo.8 

20.6 

£ 
S0.4 

5  0.2 

S 

s 

s 

/> 

yf 

^ 

/* 

/\ 

J3* 

/ 

• 

D 

iame 

ter  o 

i  Wi 

•e 

.233 

cm. 

20     22    24     26    28     30     32     34    36 

Kilo- Volts  Effective 


20     22    24     26     28    30     32    34     36 

Kilo-Volts  EffectL7.e 


FIG.  72.  FIG.  73. 

Figs.  72  and  73. — Diameter  of  corona  (0.233  cm.  wire  in  18.6  cm.  cylinder). 

appears  to  take  immediately  a  definite  finite  thickness;  the  rate 
of  increase  is  then  quite  rapid,  but  gradually  assumes  a  linear 
relation. 


1  In  Fig.  73  is  a  curve  through  the  same  points.  Throughout  this  curve 
the  correction  of  1.18  has  been  used  to  include  the  ultraviolet.  How- 
ever, near  the  starting  voltage  the  corona  seems  to  be  very  largely 
ultraviolet.  This  explains  the  low  point  at  22.5  kv. 


76  DIELECTRIC  PHENOMENA 

A  study  of  the  power  loss  equation  leads  one  to  suspect  that  the 
mechanism  of  corona  loss  is  more  complicated  than  might  at  first 
be  supposed.  This  is  also  indicated  by  many  peculiar  phenomena 
of  the  spark  discharge.  For  instance,  while  investigating  a.c. 
spark-over  and  corona  for  parallel  wires  it  was  observed  that  when 
the  end  shields  were  not  used,  and  the  wires  came  directly  in 
contact  with  the  wooden  wheel  supports,  corona  often  appeared 
to  bridge  completely  between  the  conductors  without  a  dynamic 
arc.  In  this  case  it  seemed  possible  that  the  corona  on  the  posi- 
tive wire  extended  out  farther  than  the  corona  on  the  negative 
wire  and  that  the  positive  discharges  overlapped  and  combine  in 
the  eye,  giving  the  effect  of  a  single  discharge  completely  across 
between  the  conductors. 

In  the  hope  of  throwing  further  light  on  the  discharge  and  loss 
mechanism,  an  investigation  of  corona  and  spark  was  made 
with  the  help  of  the  stroboscope.  • 

A  needle  gap  was  first  arranged  across  the  transformer  with  a 
high  steadying  resistance.  The  impressed  voltage  was  adjusted 
until  corona  appeared  all  the  way  between  the  conductors  as  in 
Fig.  74. 

Examination  of  this  was  then  made  through  the  stroboscope 
which  w|is  so  set  that  the  right  needle,  Fig.  74(2),  was  seen  when 
positive,  and  the  left  when  negative.  To  the  eye,  the  discharge 
from  the  positive  needle  has  a  bluish-white  color  and  extends  out  a 
considerable  distance,  the  negative  appears  as  a  red  and  hot  point. 
This  arrangement  may,  therefore,  be  used  as  a  rectifier.  The 
photograph  shows  more  of  the  negative  than  is  seen  by  the 
eye.  Fig.  74(1)  is  the  discharge  as  it  appears  without  strobo- 
scope, 74(2)  with  the  right  needle  as  positive,  74(3)  with  strobo- 
scope shifted  180  deg.  to  show  left  needle  as  positive.  In  74(4) 
the  stroboscope  has  the  same  position  as  74(3),  but  the  voltage  is 
higher,  and  many  fine  " static"  sparks  can  be  seen. 

If  voltage  above  the  visual  corona  point  is  impressed  on  two 
parallel  polished  wires  a  more  or  less  even  glow  appears  around  the 
wires.  After  a  time  the  wires  have  a  beaded  appearance.  On 
closer  examination  the  beads  appear  as  reddish  tufts,  while  in 
between  them  appears  a  fine  bluish- white  needle-like  fringe.  On 
examination  through  the  stroboscope  it  can  be  seen  that  the  more 
or  less  evenly  spaced  beads  are  on  the  negative  wire,  while  the 
positive  wire  has  the  appearance,  if  not  roughened  by  points,  of  a 
smooth  bluish- white  glow.  At  " points"  the  positive  discharge 
extends  out  at  a  great  distance  in  the  form  of  needles ;  it  is  possible 
that  it  always  extends  out  but  is  not  always  visible  except  as  sur- 


DIAMETER  OF  CORONA. 

FIG.  69  (Upper). — Diameter  of  corona  on  0.233  cm.  wire  in  18.6  cm. 
cylinder.  ev  =21.5  kv.  Glass  lens  kilovolts  22.5,  25,  27.5,  30,  32.5 
respectively.  (Whitehead.) 

FIG.  70  (Middle). — Diameter  of  corona  showing  effect  of  ultra-violet. 
(n),  0.232  cm.  (6),  0.316  cm.  (c),  0.399  cm.  Left  side  of  (a)(6)(c), 
quartz  lens.  Right  side  of  (a)(fe)(c),  glass  lens.  (Whitehead.) 

FIG.  71  (Lower). — Corona  on  0.233  cm.  wire,  at  22.5,  27.5,  32.5  kv.     ev 
=  20.75kv.     Glass  lens.     (Whitehead.) 

(Facing  page  76.) 


(1)  Without  stroboscope,  72,000  volts. 


Left  (-) 


(2)  With  stroboscope,  72,000  volts. 


Right  (+) 


Left  (+) 


(3)  Same  as  (2),  stroboscope  rotated  180°. 


Right  (-) 


Left  (+)  (4)  Same  as  (3),  voltage  increased  to  84,000. 

FIG.  74. — Corona  between  copper  needle  points.    20.5  cm.  gap 


Right  (-) 


(1)  Without  stroboscope. 


(+) 


(2)  With  stroboscope. 


Right  (-) 


Left  (-) 


(3)  With  stroboscope 
rotated  180°. 


Right  (+) 


FIG.  77.  —  Corona  on  parallel  wires.     No.  13  B.  and  S.  copper  wire.     Spacing, 
12.7cm.     Volts,  82,000. 


Left(-)  Right  (  +  ) 

FIG.  79. — Polished  brass  rod.  Diameter,  0.475 
cm.  Spacing,  120  cm.,  Volts,  150,000.  Note  that 
negative  "beads"  are  just  starting  to  form. 


FIG.  78. — Section  of  wire 
(Fig.  77).  "Dead."  Bright 
spots  position  of  negative 
"beads." 


Left(-)  Right  (  +  ) 

FIG.  80. — Copper  wire.  Diameter  0.26cm.  Spac- 
ing, 120  cm.  Volts,  200,000.  Polished  at  start. 
Note  negative  corona  apparently  following  spiral 

(Following  Fig.  77.) 


: grain"  of  wire. 


VISUAL  CORONA  77 

face  glow.  Thus,  the  appearance  of  beads  and  fringe  to  the  un- 
aided eye  is  really  a  combination  of  positive  and  negative  corona. 
In  Figs.  75  and  76  two  wires  are  placed  close  together  at  the  top. 
The  bottom  is  bent  out  and  needles  are  fastened  on.  Fig.  75  is 
without  a  stroboscope.  Fig.  76  is  taken  with  a  stroboscope  set  to 
show  positive  right  and  negative  left.  Thus,  positive  and  nega- 
tive coronas  for  points  and  wires  are  directly  compared.  Fig. 
77(1)  is  taken  without  the  stroboscope,  (2)  with  right  negative, 
(3)  with  stroboscope  shifted  180  electrical  degrees  to  show  the 
right  positive.  These  wires  were,  at  the  start,  highly  polished. 
At  first  corona  appeared  quite  uniform,  but,  after  a  time,  under 
voltage,  the  reddish  negative  tufts  separated,  more  or  less  evenly 
spaced  as  shown.  24(2)  is  the  same  with  stroboscope  shifted  180 
deg.  Fig.  78  shows  a  section  without  voltage.  The  bright  spots 
are  still  polished  and  correspond  in  position  to  the  negative  tufts. 
The  space  in  between  is  oxidized.  Thus,  the  negative  discharge 
appears  to  throw  metal  or  oxide  from  the  surface  at  discharge 
points.  This  takes  place  with  either  copper  or  iron  wire. 

Fig.  79  shows  positive  and  negative  corona  on  wires  widely 
spaced  to  get  uniform  field  distribution.  A  close  examination  of 
the  negative  shows  beads  about  to  form.  Fig.  80  shows  a  similar 
pair  of  conductors.  The  negative  in  this  case  has  formed  a  spiral, 
apparently  following  the  grain  twist  of  the  conductor. 

A  large  fan-like  bluish  discharge  is  often  observed  extending 
several  inches  from  the  ends  of  transformer  bushings,  points  on 
wires,  etc.  This  discharge  has  the  appearance  of  a  bluish  spray, 
reddish  at  the  point.  The  stroboscope  shows  that  the  bluish 
spray  is  positive,  while  the  red  point  at  the  base  of  the  spray  is 
negative.  Fig.  81  shows  one  of  two  parallel  polished  rods  (120 
cm.  spacing),  supported  at  the  top  and  brought  to  sharp  points 
at  the  bottom;  81(1)  shows  how  each  wire  appears  without 
stroboscope;  81(2)  is  the  wire  when  positive,  81(3)  the  wire  when 
negative.  Note  the  dark  space  on  81(3)  between  the  point  and 
negative  corona  spiral  of  tufts.  81(1)  shows  this  space  to  have 
only  the  positive  glow. 

Water  Was  placed  on  a  pair  of  parallel  conductors.  At  the  wet 
places  the  positive  corona  extended  out  in  long  fine  bluish-white 
streamers.  (See  Fig.  82  without  stroboscope.)  With  certain  forms 
of  dirt  on  the  wires  the  negative  corona  appears  as  red  spots,  the 
positive  always  as  streamers.  It  is  also  interesting  to  note  that 
if  a  uniformly  rough  wire  is  taken,  as  a  galvanized  wire  or 


78  DIELECTRIC  PHENOMENA 

" weathered"  wire,  the  positive  appears  as  bluish  needles,  while 
the  reddish  negative  is  more  uniform  than  on  the  "  corona-spotted  " 
polished  wire,  in  which  case  the  negative  corona  appears  as  con- 
centrated at  the  non-oxidized  spots.  It  is  probable  that  the 
polished  spots  are  kept  so  by  metal  and  oxide  being  "  thrown  out" 
at  the  negative,  as  suggested  above. 

Mechanical  Vibration  of  Conductors  and  Other  Phenomena. — 
Several  years  ago  a  pair  of  20  mil  steel  conductors,  500  ft.  long, 
were  strung  at  about  10-ft.  spacing,  for  power  loss  measurements. 
It  was  noticed  at  high  voltage  that  the  conductors  vibrated, 
starting  with  a  hardly  perceptible  movement,  which  in  a  few 
minutes  had  an  amplitude  of  several  feet  at  the  center  of  the  span. 
Generally  one  wire  vibrated  as  fundamental,  the  other  as  third 
harmonic.  The  period  of  the  fundamental  in  this  case  was  about 
one  per  second. 

Figs.  83  and  84  show  this  condition  repeated  in  the  laboratory 
on  short  lengths  of  conductor.  In  Fig.  83  one  wire  is  vibrating  as 
the  fundamental,  the  other  as  the  second  harmonic.  The  motion 
is  rotary.  For  the  wire  with  a  node  in  the  center,  Fig.  83,  it  is 
extremely  interesting  to  note  that  for  about  one-half  of  the  ro- 
tation the  wire  appears  very  bright,  for  the  other  half  rota- 
tion the  wirefis  much  less  bright.  This  seems  to  mean  that  each 
part  of  the  wire  is  rotating  at  the  power  supply  frequency — 60 
cycles  per  second.  Hence,  it  has  the  effect  of  the  stroboscope, 
and  for  part  of  the  rotation  there  is  always  negative  corona  and 
for  the  other  part  always  positive  corona. 

Oscillograms  of  Corona  Current. — Bennett  has  made  some  very 
interesting  oscillograms  of  corona  current.1  Fig.  8.5 (a),  (6)  and  (c) 
shows  the  voltage  wave  applied  between  a  cylinder  and  a  concen- 
tric wire,  and  the  resulting  current.  The  part  of  the  wave  above 
the  zero  line  occurs  when  the  wire  is  — ,  and  that  below  when  the 
wire  is  +;  (a)  is  for  a  voltage  very  slightly  above  the  critical 
voltage  and  shows  a  very  sudden  sharp  hump  in  the  current  wave 
when  the  wire  is  + ,  and  a  spread  out  hump  when  the  wire  is  — . 
This  gives  the  appearance  of  corona  starting  at  a  slightly  lower 
voltage  on  the  +  wire;  (6)  and  (c)  show  the  positive  and  nega- 
tive humps  at  higher  voltage.  The  oscillation  is  caused  by  the 
sudden  "corona  spark"  discharging  through  the  reactance  and 
capacity  of  the  circuit. 

Some  tests  made  on  the  starting  time  appear  to  show  that  sev- 
eral cycles  are  necessary  for  stable  conditions. 

1  Bennett,  An  Oscillographic  Study  of  Corona,  A.I.E.E.,  June,  1913. 


FIG.  83. — Mechanical  vibration  of  parallel  wires  due  to  corona. 


FIG.  84. — Mechanical  vibration  of  parallel  wires  due  to  corona. 

(Facing  page  7t 


FIG.  85. — Oscilligrams  of  corona  current.     (Bermet,  A.  I.  E.  E.,  June,  1913.) 


CHAPTER  IV 
SPARK-OVER 

By  spark-over  is  generally  meant  a  disruption  of  the  dielectric 
from  one  conductor  to  another  conductor.  Corona  is  the  same 
phenomena — spark  from  a  conductor  to  space  or  local  spark-over. 

Parallel  Wires. — If  impressed  voltage  is  gradually  increased 
on  two  parallel  wires  placed  a  considerable  distance  apart  in 
air,  so  that  the  ratio  S/r  is  above  a  certain  critical  value,  the 
first  evidence  of  stress  in  the  air  is  visual  corona.  If  the 
voltage  is  still  further  increased  the  wires  become  brighter  and 
the  corona  has  the  appearance  of  extending  farther  out  from  the  / 
surface.  Finally,  when  the  voltage  has  been  sufficiently  in- 
creased, at  some  chance  place  a  spark  will  bridge  between  the 
conductors.  When  the  spacing  is  small,  so  that  S/r  has  a  critical 
ratio,  spark  and  corona  may  occur  simultaneously,  or  the  spark 
may  bridge  across  before  corona  appears.  If  the  spacing  is  still 
further  reduced  so  that  S/r  is  below  the  critical  ratio  the  first 
evidence  of  stress  is  complete  spark-over  and  corona  never  ^ 
appears.  (See  page  27.) 

Extensive  tests  have  been  made.1  The  method  of  making  tests 
was  to  start  at  the  smaller  spacings  with  a  given  value  of  r  and 
measure  the  spark-over  voltage.  Unless  otherwise  stated  the 
frequency  used  was  60  ~.  When  the  spacings  were  above 
the  critical  ratio  of  S/r,  and  corona  formed  before  spark-over,  the 
corona  voltage  was  noted  first.  The  voltage  was  then  increased 
until  spark-over  occurred.  The  spark-over  point  is  not  as  con- 
stant or  consistent  as  the  corona  point  and  is  susceptible  to 
change  with  the  slightest  dirt  spot  on  the  conductor  surface,  and 
any  unsteady  condition  in  the  circuit,  humidity,  etc.  At  the  * 
beginning  of  the  tests  it  was  found  necessary,  in  order  to  get 
consistent  results,  to  put  water  tube  resistances  in  series  with  the 
conductors  to  eliminate  resonance  phenomena.  These  resistances 
were  high,  but  not  sufficiently  so  to  cause  an  appreciable  drop  in 
voltage  before  arc-over. 

Table  XIX  is  a  typical  data  table.  Each  point  is  the  average 
of  a  number  of  readings. 

1  See  Law  of  Corona  II,  A.I.E.E.,  June,  1912. 

79 


80 


DIELECTRIC  PHENOMENA 


TABLE  XIX. — CORONA  AND  SPARK-OVER  FOR  PARALLEL  WIRES 
Temperature  17  deg.  C.,  bar.  75.3  cm. 
Wire  No.  0,  diameter  0.825  cm. 


Test  No.  166  values  read 
60  ~ 

No.  0  wire,  corrected  to  25°  C.,  76  bar. 

Spacing 

Effective  kv.  to  neutral 

Maximum  values 
to  neutral 

Maximum 

Cm.  S 

Corona  ev 

Spark  e, 

Corona  ev 

Spark  e« 

Corona  gv 

Spark  g» 

2.54 

None 

15.8 

21.9 

41.4 

3.81 

None 

22.5 

31  2 

42.5 

5.08 

None 

27.3 

37.9 

43.2 

6.35 

None 

31.05  ' 

43.2 

43.8 

7.62 

None 

35.0 

48.5 

44.9 

8.89 

None 

37.35 

51.8 



45.0 

10.16 

40.4 

40.9 

56.0 

56.7 

44.0 

44.6 

12.70 

41.8 

42.1 

58.0 

58.1 

44.0 

44.1 

13.97 

43.7 

46.0 

60.7 

60.5 

44.2 

46.7 

15.24 

45.9 

48.1 

63.6 

67.0 

45.1 

48.9 

15.78 

46.6 

54.1 

64.8 

75.0 

43.8 

50.8 

20.32 

48.9 

59.6 

67.7 

82.8 

44.0 

53.7 

22.86 

50. 

66.2 

69.7 

91.7 

43.7 

56.8 

25.40 

51. 

71.5 

70.7 

99.2 

43.1 

60.4 

27.94 

52. 

79.0 

72.4 

109.7 

42.9 

65.1 

30.48 

53. 

84.5 

74.0 

117.0 

42.9 

67.9 

33.02 

54. 

89.6 

74.8 

124.0 

42.4 

70.2 

35.56 

55. 

95.5 

76.5 

132.5 

42.6 

73.9 

38.10 

56. 

102.3 

77.8 

141.9 

42.7 

77.8 

40.64 

57.1 

106.5 

79.4 

149.0 

42.9 

80.5 

60.96 

63.3 

87.0 

42.9 



In  columns  4  and  5  are  voltages  reduced  to  the  maximum  value 
to  neutral  and  corrected  to  standard  5.  Column  6  gives  the 
surface  gradient  for  corona.  Column  7  gives  the  surface  gradient 
for  spark,  up  to  the  spacing  where  corona  starts  first;  above  this 
critical  spacing  it  gives  the  apparent  surface  gradient  as  the 
conductor  above  this  point  must  be  larger  on  account  of  corona. 
As  the  field  around  the  conductors  at  the  small  spacings  is  very 
much  distorted  it  is  necessary  to  use  formula  12  (a)  or  12(6)  to 
calculate  the  surface  gradient. 

Fig.  86  is  a  typical  curve.  Voltage  is  plotted  with  spacing  for 
spark  and  corona.  Up  to  spacing  12.4  cm.  there  is  spark-over 
before  corona.  This  curve  seems  to  be  continuous  with  the 
corona  curve  which  starts  at  this  point.  The  spark  curve  here 


SPARK-OVER 


81 


branches  and  is  very  close  to  a  straight  line  within  the  voltage 
range.     In  Fig.  87,  the  surface  gradient  curves  are  plotted.     The 


—  150 
I  140 

1  120 
~  110 

2  100 
S  90 


50 
S  40 
5  80 

i  20 

I  10 


0   10   20   30   40   50   60  70 

Spacing  in  cm.  between  Wire  Centers 

FIG     8fi. — S:?ark-over     and     visual 
corona  voltages. 


15U 

J/i4U 

Siqn 

§110 

"100 

°"  90 

> 
•   80 

^ 

«    DU 

^* 

.2    <u 

c. 

^ 

^ 

g  co 

±      Cf> 

^xT 

Q 

a 

*L 

-   1    , 

Ud 

0   40 
o   <in 

xj 

7 

S,  d° 
5    20 

!°    lft 

t»     iU 

0       10      20      30      40      50      60     70 

Spacing  in  cm.  between  Wire  Centers 

"T. — Corona  gradient  and  ap- 
parent spark  gradient. 


(Parallel  polished  copper  wires,  0.825  cm.  diameter.     5  =  1.) 

corona  gradient  is  a  straight  line  parallel  to  the  X  axis  with  a 
slight  hump  at  the  critical  ratio  of  S/r.     The  apparent  spark 


240 

220 

200 

1 180 

% 

^  160 
1 140 

I  12° 
|  100 
!  80 

leo 

40 


,<? 


.** 


10 


25 


15  20 

Spacing  in  cm. 

FIG.  88. — Apparent  spark-over  gradients  for  parallel  wires.     (Points  meas- 
ured, curves  calculated.) 

gradient  is  also  a  straight  line,  within  the  test  range.     It  inter- 
sects the  corona  line  at  the  critical  ratio  point,  or  at  what  may  be 


82 


DIELECTRIC  PHENOMENA 


termed 'the  triangular  point,  and  extended  it  cuts  the  g  axis  at 
g  =  30.  These  are  characteristic  curves.  (See  also  Figs.  50  and 
51.)  For  a  given  spacing  the  spark-over  voltage  increases  as  the 
size  of  the  conductor  decreases. 

It  is  important  to  note  that  for  all  sizes  of  wire  the  spark  gradi- 
ent curve  extended  as  a  straight  line  cuts  the  gradient  axis  at 
approximately  g  =  30.  Spark  curves  extended  as  straight  lines 
through  the  critical  ratio  point  and  intersecting  the  gradient  axis 
at  g  =  30  are  shown  in  Fig.  88.  The  triangular  point  or  critical 
ratio  of  S/r  is  tabulated  in  Table  XX.  Its  average  value  is 

TABLE  XX. — CRITICAL  RATIOS  S/r — EXPERIMENTAL  VALUES 
Intersection  point  of  gv  and  g, 


Size, 
B.  &S. 

Radius 
cond.,  cm. 

S,  cm. 

S/r 

Size, 
B.  &S. 

Radius 
cond.,  cm. 

S.  cm. 

S/r 

0 

0.461 

13.5 

29.3 

6 

0.205 

6.2 

30.2 

0 

0.412 

11.7 

28.4 

8 

0.162 

4.8 

29.6 

2 

0.327 

10.2 

31.2 

10 

0.129 

4.0 

31.0 

4 

0.260 

7.9 

30.4 

12 

0.103 

3.0 

29.1 

5 

0.230 

7.3 

31.7 

Average 

30.1 

S/r  =  30.  If  it  is  assumed  that  the  spark-gradient  curve  is  a 
straight  line  the  conditions  are,  that  it  must  cut  the  corona 
gradient  line  at  S/r  =  30  and  extended  must  cut  the  g  axis  at 
Qo  =  30. 

The  gradient  for  gv,  or  the  gradient  at  the  triangular  point  or 
below  it,  is 


(18) 


therefore,  the  approximate  apparent  gradient  at  or  above  the 
triangular  point  is 


0.301  S 


30(  1  +  ~~r  ~  } 
\          Vr  r  ] 


per  cm.  max. 


This  follows  because  of  the  assumption  of  a  straight  line  through 
two  fixed  points. 


SPARK-OVER 


83 


The   approximate   spark-over   voltage   above   the  triangular 

point  is 

s 
ea  —  Qa  r  log  R/r  kv.  to  neutral  max. 

Below  the  triangular  point  it  may  be  found  by  substituting 
gv  for  g,. 

In  Fig.  88  each  drawn  curve  is  for  ga  values  calculated  for  vary- 
ing spacing  at  constant  radius.  The  points  are  measured  values. 
The  corona  boundary  line  is  the  gv  curve;  it  intersects  the  g. 
curves  at  S/r  =  30.  Corona  does  not  form  below  this  line,  but 
it  sparks  across  immediately.  This  is  greater  than  the  theo- 
retical ratio,  as  explained  below.  See  also  pages  27-29. 


300 
280 
260 
240 
.220 
§200 
S.180 


140 
1  120 

I100 


40 


30 


Sp; 


.05       .10       .15       .20       .25       .30       .35      .40        .45       .50 
Radius  of  Wire  iu  cm. 

FIG.  89. — Apparent    spark-over    gradients    for    parallel    wires.     (Points 
measured,  curves  calculated.) 


In  Fig.  89  each  curve  is  drawn  for  a  constant  spacing  and 
varying  radius.  The  broken  line  is  the  critical  ratio  line.  It  also 
corresponds  to  the  gv  curve.  For  spacings  below  this  line  spark 
takes  place  immediately  before  corona  forms,  and  the  ga  values 
fall  pretty  well  on  the  gv  line  as  shown  by  triangles. 

Fig.  90  is  voltage  plotted  in  the  same  way.  Below  the  corona 
boundary,  where  spark  occurs  before  corona,  the  es  curve  does  not 
hold.  The  broken  lirites  are  calculated  from  gv  and  ev.  The  points 
are  observed  values.  Thus  corona  gradient  and  spark-over  gra- 
dient, and  hence  spark  voltage  and  corona  voltage  below  S/r  =  30, 
are  the  same. 

6 


84 


DIELECTRIC  PHENOMENA 


No  great  accuracy  is  claimed  for  this  formula.  It  may,  how- 
ever, be  useful  in  approximately  determining  the  arc-over  between 
v  conductors  in  practice.  Dirt  or  water,  however,  will  greatly 
modify  the  results,  as  will  appear  below. 

The  reason  that  spark  takes  place  before  corona  can  form  at 
small  spacings  or  below  S/r  =  <*  is  discussed  on  page  27  for  con- 
centric cylinders,  in  which  case  g  was  taken  as  constant. 


IN 

"JOQO 

\ 

SHQ 

a 

X 

""v 

5  140 
2120 

00 

^ 

-J 

0 

Sp 

aci 

ii« 

"in. 

0 

30 

,c 
a 

•*~_ 

"F-; 

~~-H- 

—  a. 

—  —  . 



T^= 

T=— 

* 

-T— 

^fi 

=30 

u:   Ol) 

o 

^^ 



•*" 

10 

•3  4U 

>  on 

B 

3UI1 

dar 

r  V 

3= 

=-"- 

-^-^=' 

^=:- 

•°-- 

IX      . 

—  ~ 

d 

80 

L 

ue 

"-& 

par 

k" 

:for 

;Cc 

ron 

a 

) 

.c 

5 

.1 

0 

.1 

5 

.2 

0 

.2 

5 

.2 

0 

.£ 

5 

A 

0 

.4 

5 

.5 

0 

Eadius  ofWire  iu  cm. 

FIG.  90. — Spark-over  voltages  between  parallel  wires.     (Maximum  values 
to  neutral  given.     Points  measured,  curves  calculated.) 

We  know,  however,  that  gv  is  a  function  of  r,  and  for  air 

0.301 


r  loge  R/r 


0.301\ 

" 


Differentiating  for  maximum 

de  /          0.301 

dr  = 

or,  ev  is  maximum  when 


0.301X 
Vr) 


This  gives  a  ratio  of  R/r  greater  than  e.     The  experimental  ratio 
in  Fig.  91  is  3  and  checks  with  the  above. 

If  a  very  small  value  of  r  is  taken  corona  forms  and  then  after 
the  voltage  is  sufficiently  increased,  spark-over  occurs.     It  might 


SPARK-OVER 


85 


be  supposed  that  with  increasing  voltage  the  center  wire  would 
become  larger  and  larger  in  effect  due  to  conducting  corona  and 

r> 

finally,  when  -  -  =  critical  ratio,  spark-over  would 

radius  +  corona 

occur.  This  is  not  the  case.  It  takes  a  much  higher  voltage  for 
the  small  wire  corona  than  for  metallic  cylinders  with  R/r  at 
maximum  ratio.  Hence,  corona  seems  to  be  either  in  effect  a 


110 
100 
90 
g"80 
S70 
|60 
^60 
M  40 
30 
20 
10 

§ 

\ 

& 
\ 

1* 

S 

Par* 

•  —  , 

*y 

-- 

•  — 



r.-^: 

^>- 

„ 

t 

3 

/* 

1 

* 

/ 

y  1 
jg. 

/C 

/ 

/ 

R 

=  o 

67  ( 

m. 

/ 

1 

0  0   <N     -*      0000      C^TIJ     «3000<N-*«0      CO    0     <N     "* 
•_J,-Jr4'-ti4NNc4cN      <N    CO     M     « 

Kadius  of  Inner  Cylinder  (  r  ) 

FIG.  91. — Spark-over  and  corona  voltages  for  concentric  cylinders  with  vary- 
ing diameter  of  inner  cylinder. 

"  series  resistance,"  or  it  grades  or  distributes  the  flux  density. 
(See  Fig.   91.)     Taking  the  exact  equation  for  parallel  wires 


Cv 


s 

2r 

T   IS 

-sfe 

—    fl     1     1 

+  1        2? 

0.301  \ 

2r 

^^i    i 

Vr  )  T 

\ 

S 
2r^ 

-  cosh     2r 

(126) 


Varying  r  for  constant  S  —  10  it  is  found  that  ev  is  maximum 
when  S/r  =  6.67.  Experiments  show  this  ratio  to  be  30.  This 
is  probably  because,  at  the  small  spacing,  the  corona  acts  as  a 
flexible  conductor  which  collapses  and  forms  a  point. 

The  visual  corona  voltages,  or  the  spark-over  voltages  below 
the  critical  ratio  of  S/r  or  R/r,  should  be  of  practical  value  for 


86 


DIELECTRIC  PHENOMENA 


voltage  measurement  on  account  of  the  accuracy  at  which  they 
may  be  determined  or  calculated  for  different  temperatures,  baro- 
metric pressures,  etc. 

Influence  on  Spark-over  of  Water  and  Oil  on  the  Conductor 
Surface. — Tests  with  oil  and  water  on  the  conductor  surface  were 
made  in  a  manner  exactly  similar  to  the  dry  spark-over  and  corona 
tests.  In  the  oil  tests,  the  surface  of  the  wire  was  coated  with  a 
thin  even  film  by  means  of  an  oiled  cloth.  For  the  wet  tests, 
water  was  sprayed  on  the  conductor  surface  before  each  reading 
by  means  of  an  atomizer.  Figs.  50,  51  and  92  are  dry,  wet,  and 
oil  curves  for  three  different  sizes  of  wire. 


160 
150 

no 

ISO 

?120 

3 

|100 
*  90 


>  70 

a  eo 


S  40 


'/At 


-co 


0  10  20         30          40          50          60          70 

Sparing  in  em's,  between  Wire  Centers 

Fni.  92;  — Spark-over  and  visual  corona  for  parallel  wires.  (Diameter,  0.825 
cm.  Polished  copper.  Surfaces  dry,  wet,  and  oiled.  Maximum  volts  to 
neutral  given.) 


\ 


For  spark-over  both  water  and  oil  have  approximately  the 
same  effect.  This  curve  tends  to  approach  the  needle-gap  curve. 

For  corona,  water  very  greatly  lowers  gv.  Oil  lowers  gv  but 
to  a  much  less  extent  than  water.  Where  the  conductor  is  very 
small  the  per  cent,  increase  in  diameter  due  to  oil  more  than  com- 
pensates for  the  lowering  effect. 

The  spark  gaps  which  have  been  useful  in  measuring  high  vol- 
tages will  now  be  considered. 


SPARK-OVER 


87 


The  Gap  as  a  Means  of  Measuring  High  Voltages. — A  gap 

method  of  measuring  high  voltages  is  often  desirable  in  certain 
commercial  and  experimental  tests.     A  gap  measures  the  maxi- 
mum point  of  the  voltage  wave  and  is  therefore  used  in  many 
insulation   tests    where   break- 
down  also    depends   upon  the 
maximum    voltage.     In    most 
commercial    tests  an  accuracy 
of  2  or  3  per  cent,  is  sufficient. 
A  greater  accuracy  can  be  ob- 
tained with  the  sphere  gap  for 
special  work  where  special  pre- 
cautions are  taken. 

The  Needle  Gap.— The  needle 
gap  is  unreliable  at  high  vol- 
tages because,  due  to  the  brush 
and  broken-down  air  that  pre- 
cedes the  spark-over,  variations 
are  caused  by  humidity,  oscil- 
lations, and  frequency.1 

The  needle  gap  is  also  incon- 

venient   because  needles  must         -  0  5  10  15  a,  5.5  so  86  40  45  so  5560 

be    replaced    after    each    dis-  spacing  mem. 

charge;    the    spacing    becomes  FIG.  93. 

very  large  at  high  voltages,  and 

the  calibration  varies  somewhat  with  the  sharpness  of  the  needle. 

AVERAGE  NEEDLE  SPARK-OVER  VOLTAGES 

No.  00  Needle,  5  =  1 

A.I.E.E. 


2W 

190 
180 
170 
160 
150 
140 
-130 
|120 
£110 
^100 
I    90 
5    80 
5    70 
60 
50 
40 
30 
20 
10 
• 

Hu 

lity 

Pe. 

Cents 

v5/ 

// 

f  / 

71 

.0 

// 

y  / 

/ 

57 

I/ 

i/ 

/ 

C 

ox 

2 

2 

7 

z* 

J 

| 

W 

/ 

M 

u 

/ 

6///\ 

' 

/// 

L 

w 

J//A 

* 

I 

y 

f/ 

/) 

i 

f 

/ 

Approximate 
Needle  Gap  Curves 
for  Different 
Relative  Humidity 

— 

| 

Kv.  eff. 

Spacing  (cm.) 

Kv.  eff. 

Spacing  (cm.) 

10 

1.19 

40 

6.10 

15 

1.84 

45 

7.50 

20 

2.54 

50 

9.00 

25 

3.30 

60 

11.80 

30 

4.10 

70 

14.90 

35 

5.10 

80 

18.00 

F.  W.  Peek,  Jr.,  Discussion,  A.I.E.E.,  Feb.,  1913. 
F.  W.  Peek,  Jr.,  G.  E.  Review,  May,  1913, 


88 


DIELECTRIC  PHENOMENA 


The  effect  of  humidity  is  shown  in  Fig.  93,  where  it  can  be  seen 
that  a  higher  voltage  is  required  to  spark  over  a  given  needle  gap 
when  the  humidity  is  high  than  when  it  is  low.  (Curves,  Fig.  93, 
are  intended  only  to  illustrate  this  effect.)  It  is  probable  that  the 
corona  streamers  in  humid  air  cause  a  "fog, "  and  then  agglom- 
erate the  water  particles,  which,  in  effect,  increase  the  size  of  the 
electrodes. 

All  spark-gap  curves  of  whatever  form  of  gap  must  be  cor- 
rected for  air  density — that  is,  altitude  and  temperature.  The 
spark-over  of  the  needle  gap  decreases  with  decreasing  air  density 
but  the  correction  is  erratic  and  unreliable. 

The  Sphere  Gap.1 — The  voltage  required  to  spark  over  a  given 
gap  between  spheres  increases  with  the  diameter  of  the  spheres. 

Corona  cannot  form  on  spheres,  or 
rather,  the  spark-over  point  and 
corona  point  are  coincident  if  the 
spacing  is  not  greater  than  the 
diameter  of  the  spheres.  In  prac- 
tice a  spacing  as  great  as  three 
times  the  radius  may  be  used  with- 
out appreciable  corona.  The  vol- 
tage limit  of  a  given  sphere  in  high- 
voltage  measurements  is  thus 
reached  when  a  gap  setting  greater 
than  three  times  the  radius  is  re- 
quired. For  accurate  work  it  is 
preferable  to  use  spacings  less  than 


330 


340 


•B2GO 
£240 
§220 
H200 
"180 


5  120 
WlOO 
80 
60 


Spacing  iu  cm. 


FIG. 


94.  —  Spark-over    voltages 
of  25  cm.  spheres. 


the  diameter  of  the  sphere.  This  is  especially  so  where  one  sphere 
is  grounded.  A  larger  sphere  should  then  be  used.  With 
this  space  limit  the  -first  evidence  of  stress  is  complete  spark- 
over;  corona  can  never  form,  and  all  of  the  undesirable  effects 
and  variables  due  to  brush  discharge  and  broken-down  air  are 
eliminated.  Humidity  has  no  measurable  effect. 

The  space  factor  is  relatively  small.  Several  thousand  measure- 
ments may  be  made  without  repolishing.  The  curve  may  be 
calculated.  The  only  correction  is  the  air-density  correction. 
This  has  been  investigated  and  the  results  are  given  below.  The 

1  Chubb  and  Fortiscue,  A.I.E.E.,  Feb.,  1913.  "The  Calibration  of  the 
Sphere  Gap  Voltmeter." 

F.  W.  Peek,  Jr.,  A.I.E.E.,  Feb.,  1913.  "The  Sphere  Gap  as  a  Means  of 
Measuring  High  Voltage." 

F,  W,  Peek,  Jr.,  G.  E,  Review,  May,  1913. 


v 


, 


SPARK-OVER 


89 


*  I. — SPHERE  GAP  SPARK-OVER  VOLTAGES 
6.25-cm.  Spheres 


Spacing 

Kilovolts  effective 

Om. 

In. 

Non-grounded 

Grounded 

0.5 
1.0 
1.5 

0.197 
0.394 
0.591 

12.0 
22.5 
31.5 

12.0 
22.5 
31.5 

2.0 
3.0 
4.0 

0.787 
1.181 
1.575 

41.0 
57.5 
70.5 

41.0 
56.0 
66.0 

5.0 
6.0 
7.0 

1.969 
2.362 
2.756 

81.0 
89.0 
96.0 

73.0 
79.0 
83.0 

8.0 
9.0 
10.0 

3.150 
3.543 
3  037 

102.0 
107.0 
110.0 

88.0 
90.5 
93.0 

Each  point  is  the  iverag  ^,1  *ive  readings.  Tiie  average  variation  between 
i,  mnum  and  minimum  for  a  given  setting  is  less  than  0.5  per  cent.  For 
'-i  grounded  case,  the  curves  were  made  with  the  grounded  sphere  4  to  5 
.uameters  above  ground.  See  Table  XXXIV. 

TABLE  XXII.— S.-HEKE  GAP  SPARK-OVER  VOLTAGES 
12.5-cm.  Spheres 


Spacing 


Kilovolts  effective 


Cm. 


In. 


Non-grounded 


Grounded 


0.25 

0.098 

6.5 

6.5 

0.50 

0.197 

12.0 

12.0 

1.0 

0.394 

22.0 

22.0 

1.5 

0.591 

31.5 

31.5 

2.0 

0.787 

41.0 

41.0 

3.0 

1.181 

59.0 

59.0 

4.0 

1.575 

76.0 

75.0 

5.0 

1.969 

91.0 

89.0 

6.0 

2.362 

105.0 

102.0 

7.0 

2.756 

118.0 

112.0 

8.0 

3.150 

130.0 

120.0 

9.0 

3.543 

141.0 

128.0 

10.0 

3.937 

151.0 

135.0 

12.0 

4.72 

167.0 

147.0 

15.0 

5.91 

188.0 

160.0 

17.5 

6.88 

201.0 

168.0 

20.0 

7.87 

213.0 

174.0 

90 


DIELECTRIC  PHENOMENA 


correction  is  quite  simple.  Fig.  94  gives  typical  sphere-gap  curves 
for  both  spheres  insulated  and  for  one  sphere  grounded.  Tables 
to  XXV  give  spark-over  curves  for  6.25,  12.5,  25,  50  and 
cm.  spheres  at  sea  level  (25  deg.  C.  —  76  cm.  barometer). 


TAJ        XXIIL— 


'Li^.v,   GAP  SPARK-OVER  VOLTAGES 
25-cm.  Spheres 


Spacing 

Kilovolta  effective 

Cm. 

In. 

Non-grounded 

Grounded 

0.5 
1.0 
1.5 

0.197 
0.394 
0.591 

11 

22 
32 

11 

22 
32 

2.0 
2.5 
3.0 

0.787 
0.983 
1.181 

42 
52 
61 

42 
52 
61 

4.0 
5.0 
6.0 

1.575 
1.969 
2.362 

78 
96 
112 

78 
94 
110 

7.5 
10.0 
12.5 

2.953 
3.937 
4.92 

135 
171 
203 

132 
166 
196 

15.0 
17.5 
20.0 

5.91 

6.88 
7.87 

230 
255 

278 

220 
238 
254 

22.5 
25.0 
30.0 

8.85 
9.83 
11.81 

297 
314 
339 

268 
280 
300 

40.0 

15.75 

385 

325 

Calculation  of  Curves. — The  gradient  or  stress  on  the  air  at 
the  sphere  surface,  where  it  is  greatest,  is  found  mathematically 


e_ 
~X 


(13) 


Where  e  is  the  applied  voltage  in  kilovolts,  X  is  the  spacing  in 
centimeters,  /  is  a  function  of  X/R  and  R  is  the  radius  of  the 
sphere  in  centimeters. 


SPARK-OVER 

TABLE   XXIV. — SPHERE   GAP   SPARK-OVER  VOLTAGES 
50-cm.  Spheres 


91 


Spacing 

Kilovolts  effective 

Cm. 

In. 

Non-grounded 

Grounded 

2 

0.787 

40.0' 

40 

4 

1.575 

76.5 

76 

6 

2.362 

115.5 

112 

8 

3.150 

149.0 

145 

10 

3.937 

189.0 

185 

12 

4.72 

224.3 

220 

14 

5.51 

255.5 

250 

16 

6.30 

285.0 

2752 

20 

7.87 

335.0 

320 

25 

9.83 

393.0 

377 

30 

11.81 

445.0 

420 

35 

13.80 

493.0 

456 

40 

15.75 

537.0 

489 

45 

17.72 

573.0 

516 

50 

19.19 

605.0 

541 

55 

21.65 

633.0 

561 

60 

23.62 

660.0 

579 

65 

25.60 

684.0 

594 

70 

27.56 

705.0 

608 

75 

29.55 

725.0 

619 

1  These  values  are  calculated. 

2  Spacings  above  16  cm.  are  calculated. 

Then 

g>  =  •§•  /  kv./cm. 

where  ea  is  the  spark-over  voltage  and  g«  is  the  apparent  strength 
of  air. 

/  is  found  mathematically  and  tabulated  on  page  27,  for  the 
non-grounded  and  grounded  cases.  For  the  non-grounded  case 
we  have  found  experimentally  that  g8,  the  apparent  surface  gradi- 
ent at  spark-over,  increases  with  decreasing  radius  of  sphere,  as 
gv  for  corona  on  wires  increases  for  decreasing  radius  of  wire. 


92 


DIELECTRIC  PHENOMENA 


TAPLB  ?V.  —SPHERE  GAP  SPARK-OVER  VOLTAGES 

100-cm.  Spheres 
These  values  are  calculated 


Spacing 

Kilovolts  effective 

Cm. 

In. 

Non-grounded 

Grounded 

1.0 

0.394 

20 

20 

3.0 

1.181 

60 

60 

5.0 

1.969 

100 

100 

10.0 

3.937 

195 

195 

15.0 

5.91 

283 

280 

20.0 

7.87 

364 

360 

30.0 

11.81 

520 

505 

40.0 

15.75 

650 

615 

50.0 

19.69 

770 

730 

60.0 

23.62 

870 

810 

70.0 

27.56 

956 

895 

80.0 

31.50 

1044 

956 

90.0 

35.43 

1107 

1010 

100.0 

39.37 

1182 

1057 

110.0 

43.35 

1238 

1090 

120.0 

47.20 

1290 

1133 

130.0 

51.20 

1335 

1160 

140.0 

55.70 

1378 

1189 

150.0 

59.10 

1412 

1212 

For  a  given  size  of  sphere,  gs  is  practically  constant,  independent 
of  spacing,  between  the  limits  of  X  =  0.54\/R  and  X  =  2R. 
The  average  gradient  between  these  limits  of  separation  is 


g,  =  27.2   1  + 


0.54V      , 
— 7=r)kv./cm.  max. 

VR 


gs  =  19.3/1  H ^=)kv./cm.  eff.  sine  wave.1 


(a) 
(6) 


The  maximum  variation  from  the  average  between  the  limits 
may  be  2  per  cent.  When  X  is  less  than  0.54  V^,  0«  increases  very 
rapidly  because  the  spacing  is  then  less  than  the  "rupturing  energy 
distance."1  Above  X  =  3R,  gs  apparently  gradually  increases. 

1  F.  W.  Peek,  Jr.,  "Law  of  Corona  III,"  A.I.E.E.,  June,  1913. 


SPARK-OVER  93 

This  increase  seems  only  apparent  and  due  to  the  shanks,  sur- 
rounding objects,  etc.,  better  distributing  the  flux  or  lessening  the 
flux  density.  When  both  spheres  are  insulated  and  of  practical 
size,  the  change  is  not  great  within  the  prescribed  limits.  In  this 
case  the  neutral  of  the  transformer  should  be  grounded  so  that 
spheres  are  at  equal  and  opposite  potential.  When  one  sphere 
is  grounded,  however,  this  apparent  increase  of  gradient  is  very 
great  if  the  mathematical  /,  which  does  not  take  account  of  the 
effect  of  surrounding  objects,  is  used.  For  this  reason  /  was 
found  experimentally,  assuming  ga  constant  within  the  limits,  as  it 
is  in  the  non-grounded  case,  and  finding  values  of  f0  correspond- 
ing to  the  different  values  of  X/R.'  Any  given  value  of  the  ratio 
X/R  should  require  a  constant  f0  to  keep  g8  constant  independent 
of  R.  This  was  found  to  check.1 

The  curves  may  be  approximately  calculated  thus: 

_      z  (non-grounded)  m  * 

"  g*  f     effective  sine  wave. 

-  n  —  (grounded) 

"  gs  f0      effective  sine  wave. 

Where  gs  is  calculated  from  the  equation  (6)  ,  and  /  or  f0  are  found 
from  the  table  on  page  27  for  the  given  X/R.  These  equations 
have  been  given  for  theoretical  rather  than  practical  reasons. 
Curves  should  be  calculated  only  when  standard  measured  curves  can- 
not be  obtained.  Measured  curves  are  given  here.  The  average 
error,  however,  for  curves  calculated  from  the  above  equations,  for 
2-cm.  diameter  spheres  and  over,  should  not  be  greater  then  2  per 
cent.  The  accuracy  of  calculations  is  not  as  great  as  in  the  case 
of  the  starting  point  of  corona  on  wires. 

The  Effect  of  Air  Density  or  Altitude  and  Temperature:  Cor- 
rection Factor.  Practical  Application.  —  We  have  found  that  the 
average  gradient  for  various  air  densities  may  be  expressed 


g,  =  27.261  +  -Skv./cm.  max. 


ga  =  19.36/1  +  -^iVv./cm.  effective. 

\     Vm/ 

where  5  is  the  relative  air  density.  (See  page  51.)  This  correc- 
tion does  not  apply  for  small  spacings  at  low  air  density.  (See 
page  196.) 

If0  was  determined  with  the  grounded  sphere  4  to  5  diameters  above 
ground.  In  practice,  this  may  vary  from  4  to  10  diameters  without  great 
error.  See  Table  XXXIV.  Voltage  values  in  tables  correspond  to  4  to  5 
diameters  above  the  ground  for  this  case. 


94 


DIELECTRIC  PHENOMENA 


The  standard  curve  may  be  made  to  apply  to  any  given  altitude 
by  multiplying  the  standard  curve  voltage  at  different  spacings 
by  the  correction  factor  thus 


19.; 


19.31 


_ 

VdR  +  0.54 

VR  +  0.54 


TABLE  XXVI 


ea 


Approximate 
corresponding 
altitude 

Barometer 

Values  of  a  at  25  deg.  C.  for  standard  spheres  of  the 
following  diameter,  cm. 

Cm.,  Hg   In.,  Hg 

Ft. 

6.25 

12.5 

25.0 

37.5 

50.0 

75.0 

100  0 

0 
500 
1,000 

76.00 
74.58 
73.14 

29.92 
29.36 
28.79 

1.000 
0.981 
0.964 

1.000 
0.980 
0.963 

1.000 
0.980 
0.962 

1.000 
0.979 
0.961 

1.000 
0.979 
0.960 

1.000 
0.979 
0.960 

1.000 
0.979 
0.960 

1,500 
2,000 
2,500 

71.77 

70.42 
60.09 

28.25 
27.72 
27.20 

0.948 
0.932 
0.916 

0.946 
0.929 
0.913 

0.945 
0.927 
0.911 

0.944 
0.926 
0.909 

0.943 
0.925 
0.908 

0.942 
0.924 
0.907 

0.942 
0.924 
0.907 

3,000 
3,500 
4,000 

67,74 
66.51 
65.25 

26.67 
26.18 
25.69 

0.902 
0.887 
0.873 

0.899 
0.884 
0.870 

0.897 
0.882 
0.867 

0.895 
0.880 
0.865 

0.893 
0.878 
0.863 

0.892 
0.876 
0.861 

0.891 
0.875 
0.860 

4,500 
5,000 
6,000 

64.01 
62.79 
60.45 

25.23 
24.72 
23.80 

0.859 
0.845 
0.817 

0.855 
0.841 
0.812 

0.852 
0.838 
0.808 

0.850 
0.835 
0.805 

0.848 
0.833 
0.803 

0.846 
0.831 
0.801 

0.845 
0.830 
0.800 

7,000 
8,000 
9,000 

58.22 
56.03 
53.84 

22.93 
22.05 
21.20 

0.791 
0.765 
0.739 

0.786 
0.759 
0.733 

0.782 
0.754 
0.728 

0.779 
0.750 
0.724 

0.776 
0.748 
0.721 

0.774 
0.746 
0.719 

0.772 
0.744 
0.717 

10,000 
12,000 
15,000 

51.85 

48  ..09 
42.88 

20.41 
18.93 
16.88 

0.716 
0.669 
0.606 

0.709 
0.661 
0.596 

0.703 
0.656 
0.589 

0.698 
0.651 
0.585 

0.694 
0.647 
0.580 

0.692 
0.644 
0.577 

0.690 
0.642 
0.575 

In  order  to  avoid  the  trouble  of  calculating  in  practice,  the 
factor  is  tabulated  in  Tables  XXVI  and  XXVII.  This  correc- 
tion is  very  accurate.  Table  XXVI  gives  the  correction  factor 
for  different  sizes  of  spheres  at  different  barometric  pressure  and 
at  constant  temperature.  When  the  voltage  strikes  across  a 


SPARK-OVER 


95 


given  gap  the  voltage,  e,  corresponding  to  the  gap  is  found  from 

the  standard  curve  and  multiplied  by  the  correction  factor  a,  or 

a  curve  may  be  plotted  corresponding  to  a  given  barometric 

pressure. 

Thus  el  =  ea 

Table  XXVII  gives  the  correction  factor  for  various  values  of 
6.  5  may  be  calculated  for  the  given  temperature  and  barometric 
pressure  and  correction  factor  then  found  from  the  table.  Fig.  95 
gives  the  standard  curve  for  the  25-cm.  sphere  (non-grounded) 
(25  deg.  C.,  76  cm.  bar.  pressure)  and  curves  calculated  therefrom 
for  25  deg.  C.  and  various  barometric  pressures. 


TABLE  XXVII.  —  CALCULATED  VALUES  OF  a  FOR  DIFFERENT  VALUES  OF  5 


a  =  V* 


0.54 


Relative 
air  density 


Values  of  a 
Diameter  of  standard  spheres  in  cm. 


d 

6.25 

12.5 

25.0 

37.5 

50.0 

75.0 

100.0 

0.50 
0.55 
0.60 

0.547 
0.594 
0.640 

0.535 
0.583 
0.630 

0.527 
0.575 
0.623 

0.522 
0.570 
0.618 

0.519 
0.567 
0.615 

0.517 
0.565 
0.613 

0.516 
0.564 
0.612 

0.65 
0.70 
0.75 

0.686 
0.732 
0.777 

0.677 
0.724 
0.771 

0.670 
0.718 
0.766 

0.665 
0.714 
0.*762 

0.663 
0.711 
0.759 

0.661 
0.709 
0.757 

0.660 
0.708 
0.756 

0.80 
0.85 
0.90 

0.821 
0.866 
0.910 

0.816 
0.862 
0.908 

0.812 
0.859 
0.906 

0.809 
0.857 
0.905 

0.807 
0.855 
0.904 

0.805 
0.854 
0.903 

0.804 
0.853 
0.902 

0.95 
1.00 
1.05 

0.956 
1.000 
1.044 

0.955 
1.000 
1.045 

0.954 
1.000 
1.046 

0.953 
1.000 
1.047 

0.952 
1.000 
1.048 

0.951 
1.000 
1.049 

0.951 
1.000 
1.049 

1.10 

1.092 

1.092 

1.094 

1.095 

1.096 

1.097 

1.098 

Experimental  Determination  of  the  Effect  of  Air  Density. — The 
equation  for  the  air  density  correction  factor  was  determined  by 
an  extensive  investigation  of  the  spark-over  of  spheres  in  a  large 
wooden  cask  arranged  for  exhaustion  of  air.  This  cask  was 
built  of  paraffined  wood  and  was  2.1  meters  high  by  1.8  meters  in 
diameter  inside.  (See  Fig.  96.) 


96 


DIELECTRIC  PHENOMENA 


Tests  were  made  by  setting  a  given  size  of  sphere  at  a  given 
spacing,  gradually  exhausting  the  cask,  and  reading  spark-over 


200 

180 

1GO 

1 140 

§120 

1 100 

2.  80 
i2 
60 

40 
20 


&     10    12    14    16    IS   20 

Spacing  cm. 


FIG.  95. — Sphere  gap  spark-over  voltages  at  various  air  pressures.     (12.5 
cm.  spheres.     Non-grounded.     Curves  calculated.     Points  measured.) 

voltage  at  intervals  as  the  air  pressure  was  changed.     (Tem- 
perature was  always  read,  but  varied  only  between  16  deg.  and 


FIG.  96. — Cask  for  the  study  of  the  variation  of  spark-over  and  corona 
voltages  with  air  pressure. 

21  deg.  C.)     This  was  repeated  for  various  spacings  on  spheres 
ranging  in  diameter  from  2  cm.  to  25  cm.     At  the  start,  the 


SPARK-OVER 


97 


possible  effect  of  spark-overs  on  the  succeeding  ones  in  the  cask 
was  investigated  and  found  to  be  nil  or  negligible.  A  resistance 
of  1  to  4  ohms  per  volt  was  used  in  series  with  the  spheres.  Wave 
shape  was  measured  and  corrected  for.  Voltage  was  read  on  a 
voltmeter  coil,  by  step-down  transformer  and  by  ratio.  Pre- 
cautions were  taken  as  noted  in  other  chapters. 

In  order  to  illustrate  the  method  of  recording  data,  etc.,  a  small 
part  of  the  data  for  various  spheres  and  spacings  is  given  in  Tables 
XXVIII  to  XXXII.  Considerable  data  are  plotted  in  curves, 
Figs.  97  to  99.  The  points  are  measured  values.  The  drawn 
lines  are  calculated  by  multiplying  the  voltage  values  from  the 
standard  curves  at  5  =  1,  by  the  correction  factor. 

TABLE  XXVIII. — SPHERE   GAP    SPARK-OVER    VOLTAGES  AND   GRADIENT 
2.54-cm.  Spheres.     Non-grounded 
Barometer  75.5 


Spacing 

Temp. 

Press.,  cm. 
of'Hg 

Relative 
air 
density 

Kv. 

Oi  measured 

Cm. 

In. 

Eff. 

Max. 

Eff. 

Max. 

0.635 

0.25 

15° 

75.5 

72.6 
70.5 

68.4 
65.8 
62.6 

60.0 
56.7 
54.8 

52.6 
50.5 
47.6 

45.4 
42.4 
40.0 
36.8 

1.028 

0.990 
0.957 

0.930. 
0.895 
0.852 

0.818 
-  0.776 
0.745 

0.717 
0.686 
0.649 

0.618 
0.576 
0.544 
0.500 

15.7 
15.3 
14.9 

14.4 
14.0 
13.6 

13.2 
12.5 
"12.1 

11.8 
11.3 
10.7 

10.4 

9.8 
9.3 

8.7 

22.2 
21.6 
21.1 

20.4 
19.8 
19.2 

18-.  7 
17.2 
17.1 

16.7 
16.0 
15.2 

14.7 
13.8 
13.1 
12.2 

29.2 
28.5 
27.7 

26.8 
26.0 
25.3 

24.6 
23.2 
22.5 

22.0 
21.0 
20.0 

19.3 
18.2 
17.2 

ie:i 

41.3 
40.3 
39.2 

38.0 
,36.8 
35.7 

34.8 
32.0 
31.8 

31.1 

29.8 
28.3 

27.4 
25.8 
24.4 

22.8 

...... 

:• 

98 


DIELECTRIC  PHENOMENA 


TABLE  XXIX. — SPHERE  GAP  SPARK-OVER  VOLTAGES  AND  GRADIENTS 
5.08  Spheres.     Non-grounded 


Spacing 

Relative 
air 
density 

Kv. 

g»  measured 

Cm. 

In. 

Effective 

Maximum 

Effective 

Maximum 

5.08 

2 

1.018 

78.4 

111.0 

27.4 

38.9 

5.08 

2 

0.980 

75.6 

107.0 

26.5 

37.6 

5.08 

2 

0.944 

73.1 

103.5 

25.6 

36.2 

5.08 

2 

0.903 

70.7 

100.0 

24.8 

35.0 

5.08 

2 

0.872 

68.7 

97.2 

24.0 

34.0 

5.08 

2 

0.836 

64.0 

90.5 

22.4 

31.7 

5.08 

2 

0.798 

63.6 

90.0 

22.3 

31.5 

5.08 

2 

0.764 

61.1 

86.4 

21.4 

30.2 

5.08 

2 

0.726 

58.9 

83.3 

20.6 

29.2 

5.08 

2 

0.682 

56.1 

80.5 

19.6 

28.2 

5.08 

2 

0.654 

54.0 

76.4 

18.9 

26.8 

5.08 

2 

0.618 

51.5 

73.0 

18.0 

25.6 

5.08 

2 

0.578 

49.0 

69.3 

17.2 

24.3 

5.08 

2 

0.544 

45.8 

64.7 

16.0 

22.6 

5.08 

2 

0.510 

43.3 

61.2 

15.2 

21.4 

TABLE  XXX. — SPHERE  GAP  SPARK-OVER  VOLTAGES  AND  GRADIENTS 
12.5-cm.  Spheres.     Non-grounded 


Spacing 

Relative 
air 
density 

Kv. 

Us  measured 

Cm. 

In. 

Effective 

Maximum 

Effective 

Maximum 

12.7 

5 

0.982 

163.0 

230.0 

23.1 

32.7 

12.7 

5 

0.951 

156.0 

221.0 

22.2 

31.4 

12.7 

5 

0.917 

150.0 

212.5 

21.3 

30.2 

12.7 

5 

0.880 

147.0 

208.0 

20.9 

29.5 

12.7 

5 

0.846 

143.5 

203.0 

20.4 

29.8 

12.7 

5 

0.807 

139.5 

197.5 

19.8 

28.0 

12.7 

5 

0.780 

134.5 

190.0 

19.1 

27.0 

12.7 

5 

0.736 

131.0 

185.5 

18.6 

26.3 

12.7 

5 

0.699 

125.0 

177.0 

17.7 

25.1 

12.7 

5 

0.666 

120.5 

170.0 

17.1 

24.2 

12.7 

5 

0.637 

115.5 

163.0 

16.4 

23.1 

12.7 

5 

0.598 

109.5 

155.0 

15.5 

22.0 

12.7 

5 

0.561 

104.5 

147.5 

14.8 

21.0 

12.7 

5 

0.541 

101.0 

142.5 

14.3 

20.2 

SPARK-OVER-,  ;  ;  ^  >/:  \  £  99 


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Eelative  Air  Density    5 

FIG.  97. — Spark-over  voltages  at  different  air  densities.     (12 . 5  cm.  spheres 
non-grounded.     Figures  on  curves  denote  spacing.) 


TABLE  XXXI. — SPHERE  GAP  SPARK-OVER  VOLTAGES  AND  GRADIENTS 
12.5-cm.  Spheres.     Grounded 


Spacing 

Relative 
air 
density 

Kv. 

g,  measured 

Cm. 

In. 

Effective 

Maximum 

Effective 

Maximum 

6.35 

2.5 

0.908 

95.5 

135.0 

21.2 

30.0 

6.35 

2.5 

0.869 

92.5 

130.5 

20.5 

29.0 

6.35 

2.5 

0.828 

88.6 

125.0 

19.7 

27.8 

6.35 

2.5 

0.796 

85.8 

121.0 

19.0 

26.9 

6.35 

2.5 

0.758 

81.1 

114.5 

18.0 

25.4 

6.35 

2.5 

0.723 

78.2 

110.5 

17.3 

24.5 

6.35 

2.5 

0.690 

73.2 

103.5 

16.2 

23.0 

6.35 

2.5 

0.653 

71.5 

101.0 

15.9 

22.4 

6.35 

2.5 

0.620 

68.2 

96.3 

15.1 

21.4 

6.35 

2.5 

0.582 

64.3 

90.9 

14.2 

20.2 

6.35 

2.5 

0.539 

60.7 

85.8 

13.5 

19.0 

6.35 

2.5 

0.439 

55.6 

78.5 

12.3 

17.4 

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^TRIC  PHENOMENA 


0    0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1.0 

Relative  Air  Density  0 


0    2     4     6     8    10  12  14  16   18   20  22  24  26 

Diameter  of  Spheres  cm. 

FIG.  98.  FIG.  99. 

Spark-over  gradients  at  different  air  densities  for  several  sizes  of  spheres. 

(Points  measured*     Curves  calculated  from  gs  =  19.36(1  -|  —  ~r==]  ) 

TABLE  XXXII.  —  SPHERE  GAP  SPARK-OVER  VOLTAGES  AND  GRADIENTS 
25-cm.  Spheres.     Non-grounded 


Spacing 

Relative 
air 
density 

Kv. 

g»  measured 

Cm. 

In. 

Effective 

Maximum 

Effective 

Maximum 

7.62 

3 

1.018 

139.0 

196.5 

22.2 

31.5 

7.62 

3 

0.978 

133.5 

189.0 

21.4 

30.3 

7.62 

3 

0.942 

129.5 

183.0 

20.8 

29.3 

7.62 

3 

0.906 

126.0 

178.0 

20.2 

28.5 

7.62 

3 

0.888 

121.5 

172.0 

19.5 

27.6 

7.62 

3 

0.839 

115.0 

163.0 

18.4 

26.1 

7.62 

3 

0.796 

111.0 

157.0 

17.8 

25.2 

7.62 

3 

0.752 

105.5 

149.0 

16.9 

23.9 

7.62 

3 

0.718 

101.5 

142.0 

16.3 

22.7 

7.62 

3 

0.685 

96.2 

136.0 

15.4 

21.8 

7.62 

3 

0.646 

91.5 

129.5 

14.6 

20.7 

7.62 

3 

0.608 

87.0 

123.0 

13.9 

19.7 

7.62 

3 

0.570 

81.3 

115.0 

13.0 

18.4 

7.62 

3 

0.527 

74.7 

105.5 

12.0 

16.9 

7.62 

3 

0.491 

70.8 

100.0 

11.3 

16.0 

SPARKvQVER 


101 


The   calculated  values  check  the   measured   values   closely. 

The  equation  for  the  correction  factor  was  deduced  from  meas- 
ured values  as  follows: 

From  a  former  investigation  it  was  found  that  at  5  =  1  the 
average  gradient 


From  this  investigation  it  was  found  that  the  average  gradient 
at  various  values  of  5  is 


TABLE     XXXIII. — AVERAGE     EFFECTIVE     RUPTURING     GRADIENT     FOR 

SPHERES  OF  SEVERAL  DIAMETERS  AND  VARYING  AIR  DENSITIES 

Diameter  of  Spheres,  cm.     Surface  Gradients 

/         0  54  \ 
Columns  marked  "Calc."  are  from,  ga  =  19.36(  1  H 7 — •  ) 

VSR/ 


2.54 

5.08 

12.5 

25 

Meas. 

Calc. 

Meas. 

Calc. 

Meas. 

Calc. 

Meas. 

Calc. 

1,00 

28.7 

28.5 

25.8 

25.8 

24.0 

23.4 

21.9 

22.2 

0.90 

26.2 

26.1 

23.7 

23.3 

21.8 

21.2 

19.9 

20.1 

0.80 

24.0 

23.7 

21.3 

21.3 

19.6 

19.1 

17.9 

18.0 

0.70 

21.3 

21.2 

19.0 

19.0 

17.4 

16.9 

15.7 

15.9 

0.60 

18,7 

18.7 

16.7 

16.6 

15.2 

14.7 

13.6 

13.8 

0.50 

16.1 

16.1 

14.6 

14.3 

13.0 

12.5 

11.6 

11.7 

The  average  measured  gradients  for  various  values  of  6  are  given 
in  Table  XXXIII,  the  calculated  values  from  the  equation  are 
also  given.  The  check  is  quite  close.  It  should  be  remembered, 
however,  that  these  are  average  values  over  this  range  of  spacing 
and  that  there  is  a  small  variation  at  different  spacings  as  already 
explained.  (See  Figs.  98  and  99.) 

Precautions  against  Oscillations  in  Testing. — A  non-inductive 
resistance  of  1  or  4  ohms  per  volt  should  always  be  placed 
directly  in  series  with  the  gap.  For  the  non-grounded  gap,  one- 
half  should  be  placed  on  each  side.  When  one  gap  is  grounded 
all  of  the  resistance  should  be  placed  on  the  insulated  side.  One 

1  F.  W.  Peek,  Jr.,  "Law  of  Corona  III,"  A.I.E.E.,  June,  1913. 
F,  W.  Peek,  Jr.,  Discussion,  A.I.E.E.,  Feb.,  1913. 
7 


1  02 


object  of  the  resistance  is  to  prevent  oscillations  from  the  test 
piece,  as  a  partial  arc-over  on  a  line  insulator,  reaching  the  gap. 
Another  object  is  to  limit  the  current  discharge.  This  resist- 
ance is  of  special  importance  when  tests  are  being  made  on  appa- 
ratus containing  inductance  and  capacity.  If  there  is  no  resist- 
ance, when  the  gap  sparks  over,  oscillations  will  be  produced 
which  will  cause  a  very  high  local  voltage  rise  over  parts  of  the 
winding.  If  sufficient  resistance  is  used  these  oscillations  will  be 
damped  out.  This  is  illustrated  in  Fig.  100,  which  shows  results 
of  -a  test  on  a  high-  voltage  transformer. 


r  W  =  0.12  Ohms  per  Volt 
v  W  =  0.25  Ohms  per  Volt 

tw   =  Very  Small 

I  u  =  1  Ohm  per  Volt 

FIG.  100. 


Referring  to  Fig.  100,  the  high- voltage  winding  of  the  trans- 
former under  test  is  short  circuited  and  connected  to  one  terminal 
of  the  testing  transformer.  The  other  side  of  the  testing  trans- 
former is  grounded.  The  low- volt  age  winding  of  the  transformer 
under  test  is  short  circuited,  connected  to  the  case  and  ground. 
Voltage  is  gradually  applied  to  the  transformer  under  test  until 
the  " measuring  gap"  sparks  over.  Insulated  taps,  1,  2,  3,  4,  5, 
are  brought  out  at  equally  spaced  points  on  the  high-tension 
winding  of  the  transformer  under  test.  Auxiliary  needle  gaps 


SPARK-OVER  103 

are  placed  between  1  and  2,  2  and  3,  and  1  and  3,  to  measure  the 
voltage  which  appears  across  these  sections  of  the  winding  when 
the  main  measuring  gap  discharges.  The  numbers  between 
1-2,  2-3,  and  1-3  represent  the  sparking  distances  of  the  local 
voltages  caused  by  a  discharge  of  the  measuring  gap.  Four 
cases  are  given  with  different  values  of  resistance  co  in  the  main 
gap.  When  co  =  1  ohm  per  volt,  the  local  oscillations  are 
completely  damped  out. 

With  small  resistance  in  the  gap,  a  19-cm.  spark-over  causes  a 
voltage  to  build  up  between  coils  1  and  3  (which  sparks  over 
a  150-cm.  gap),  although  the  total  applied  voltage  across  the 
transformer  is  only  equivalent  to  a  19-cm.  gap.  The  apparatus 
may  thus  be  subjected  to  strains  far  beyond  reason,  and  either 
broken  down  or  very  much  weakened.  Water-tube  resistance  is 
the  most  reliable.  A  metallic  resistance,  if  non-inductive  and  of 
small  capacity,  may  be  used.  Carbon  or  graphite  rods  should  be 
avoided  as,  although  they  may  measure  up  to  a  very  high  re- 
sistance  at  low  voltage,  the  resistance  may  become  very  low  at 
high  voltage  by  " coherer"  action. 

When  the  tested  apparatus  is  such  that  there  is  considerable 
incipient  arcing  before  spark-over,  it  is  better  to  use  the  sphere  to 
determine  the  " equivalent"  ratio  of  the  transformer  at  a  point 
in  voltage  below  the  voltage  at  which  this  arcing  occurs.  The 
sphere  gap  should  then  be  widened  out,  the  spark-over  voltage 
measured  on  the  low-voltage  side  of  the  transformer  or  in  the 
voltmeter  coil,  and  multiplied  by  this  equivalent  ratio.  It  must 
also  be  remembered  that  resistances  do  not  dampen  out  low 
frequency  surges  resulting  from  a  short  circuit,  etc. 

Miscellaneous  Precautions. — In  making  tests  it  is  desirable 
to  observe  the  following  precautions: 

The  shanks  should  not  be  greater  in  diameter  than  one-fifth  the 
sphere  diameter.  Metal  collars,  etc.,  through  which  the  shanks 
extend  should  be  as  small  as  practicable,  and  not  come  closer  to 
the  sphere  than  the  gap  distance  at  maximum  opening.  The 
effect  of  a  large  plate  or  plates  on  the  shanks  is  given  in  Table 
XXXIV.  The  sphere  diameter  should  not  vary  more  than  0.1 
per  cent.,  and  the  curvature,  measured  by  a  spherometer,  should 
not  vary  more  than  1  per  cent,  from  that  of  a  true  sphere  of  the 
required  diameter.  The  spheres  should  be  at  least  twice  the 
gap  setting  from  surroundings.  This  is  especially  important  if 
the  objects  are  large  conducting,  or  semi-conducting  masses, 


104 


DIELECTRIC  PHENOMENA 


walls,  floor,  etc.  Care  must  also  be  taken  to  so  place  the 
spheres  that  external  fields  are  not  superposed  upon  the  sphere 
gap.  This  is  likely  to  result,  especially  in  the  nongrounded 
case,  from  a  large  mass  of  resistance  units  or  connecting  leads, 
etc.,  in  back  of  and  in  electrical  connection  with  either  sphere. 
The  error"  may  be  plus  or  minus  as  indicated  for  the  small  plates 
in  Table  XXXIV.  With  the  water  tube  resistance  this  condi- 
tion is  not  likely  to  obtain  as  the  tube  may  be  brought  directly 
to  the  sphere  as  an  extension  of  the  shank.  Great  precautions 

TABLE  XXXIV. — EFFECT  OF  METAL  PLATES  ON  THE  SHANKS.     DISTANCE 

TO   GROUND   ON   ARC-OVER — OF   6.25-CM.    SPHERES 

Per  Cent.  Change  of  Voltage 


Non-rgrounded  5  cm.  diameter 

Grounded  5  cm.  diameter  plates. 

Sphere 

plates.    6.25  cm.  back  of 

6.25  cm.  back  of 

Both  spheres 

One  sphere 

Insulated  sphere 

Grounded  sphere 

1.5 

0.0 

0.0 

+  0.7 

-0.7 

3.0 

+  1.0 

-1.0 

+  1.5 

-1.5 

6.0 

+2.0 

-2.0 

+  3.0 

-2.0 

APPROXIMATE  EFFCT  OF  DISTANCE  ABOVE  GROUND  WHEN  ONE  SPHERE  Is 

GROUNDED 


Diameters  of 
grounded  sphere 
above  ground 

Percentage  variation  from  standard  curves  for  different  spacings 

-  x  =  2R 

*  =  R 

R 

X  =  2 

0 

-  10.0 

-  5.5 

0.0 

1 

-    4.5 

-  3.0 

0.0 

2 

-    2.0 

-   1.0 

0.0 

3 

-    1.0 

-  0.5 

0.0 

4 

-    0.0 

-  0.0 

0.0 

5 

+    0.5 

+  0.3 

0.0 

6 

+    1.0 

+  0.5 

0.0 

10 

+    2.5 

+  1.0 

0.0 

20 

+    2.5 

+  i.o 

0.0 

NOTE:  The  spacing,  X,  is  given  in  terms  of  radius,  R,  to  make  the  correction  applicable 
to  any  size  of  sphere.  The  distance  of  the  grounded  sphere  above  ground  is,  for  the  same 
reason,  given  in  terms  of  the  sphere  diameter.  The  ( +)  sign  means  that  a  higher  voltage 
is  required  to  arc  over  the  gap  than  that  given  by  the  standard  curve;  the  (  —  )  sign  indi- 
cates that  a  lower  voltage  is  required.  The  standard  curves  are  made  with  the  grounded 
spheres  from  4  to  5  diameters  above  ground.  In  practice  it  is  desirable  to  work  between  4 
and  10  diameters,  never  under  3.  Above  10  the  variations  in  per  cent,  error  remain  about 
the  same. 

When  both  spheres  are  insulated,  with  the  transformer  neutral  at  the  mid  point,  there  is 
practically  no  variation  in  voltage  for  different  distances  above  ground. 


SPARK-OVER 


105 


are  necessary  at  very  high  voltages  to  prevent  leakage  over 
stands,  supports,  etc.,  and  to  prevent  corona  and  brush  dis- 
charges. Unless  such  precautions  are  taken  errors  will  result. 


260 
240 

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g  180 
*S  160 
1 140 
,2120 
«100 


40 


10        20        30 


50       60       70       80       90      100 
icing  cm. 


FIG.  101. — Spark-over  voltages  between  points,     o,  dry;  A,  wet;  x,  rain. 
0 . 25"  per  minute.     60°  points  on  1 . 25  cm.  rods. 

Rain  and  Water  on  Sphere  Surface. — Figs.  101  and  102  show 
the  effect  of  rain  and  water  on  points  and  spheres.     The  ratio 


3UU 

^*- 

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1 

300 
340 

X 

x 

/ 

300 

ffi280 

/ 

X 

/ 

x^ 

/ 

x^ 

£240 
§220 

>  160 
.2140 
W120 
100 
80 
60 
40 
20 

/ 

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^ 

x-  3 

/ 

^ 

^ 

3 

( 

X* 

^ 

•^ 

/ 

~ 

x^" 

J 

^-1 

/ 

-^ 

^ 

-" 

/ 

^ 

^ 

^ 

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/ 

^ 

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^ 

/ 

^ 

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^^ 

* 

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10  15  20  25  30  35  40  45  50  55  60  65   70  75 
Spacing  cm. 


FIG.  102. — Spark-over  voltages  between  25  cm.  spheres.     1,  dry;  2,  wet 
surface;  3,  rain  (0.25"  pef  min.). 

of  dry  to  rain  (0.2  in.  per  min.)  spark-over  voltage  for  a  given 
spacing  will  average  about  2.5  for  6.25  to  50-cm.  spheres. 

High  Frequency,  Oscillations,  Impulses.— A  great  deal  of 
confusion  often  results  in  discussing  the  effects  of  "high  fre- 
quency" on  insulation  without  differentiating  between  con- 
tinuous sine  wave  high  frequency,  oscillations,  and  steep  wave 


106 


DIELECTRIC  PHENOMENA 


- 


front  impulses.     This  is  so  because  the  effects  may  be  quite  dif- 
ferent, and  .are  all  attributed  to  the  same  cause. 

High  frequency  from  an  alternator,  or  a  series  of  oscillations, 
may  cause  high-insulation  loss,  heating,  and  the  resulting  weak- 
ening of  the  insulation.  Single  trains  of  oscillations,  or  single 
impulses,  may  not  produce  heating.  Energy,  and  therefore 
definite  finite  time,  is  required  to  rupture  insulation.  For  a  single 
impulse,  or  oscillation,  where  the  time  is  limited,  a  greater  vol- 
tage should  be  required  to  break  down  a  given  insulation  than  for 
continuous  high  frequency  or  for  low  frequency.  Experiments 


24 

22 
|20 

18 


r 


12 
010 
8 
6 
4 
2 


on 

28 
26 
24 
22 

|20 

"1C 

a  io 

8 
6 
4 
2 

X 

/ 

^ 

/ 

/* 

| 

/\ 

1 

1 

/ 

X. 

X 

0  .1   .2  .3  .4    .5  .6  .7  .8   .9  1.01.1 
Spacing    cm. 

FIG.  103. — Sphere  gap  spark- 
over  voltages  at  60  cycles  and 
1000  cycles.  5 . 08  cm.  spheres. 

(Drawn  curves  60  cycles. 


0    .1  .2  .3  .4   .5  .6    .7  .8  .9  1.0  1.1 

Spacing   <MD. 

FIG.  104. — Sphere  gap  spark- 
over  voltages  at  60  cycles  and 
1000  cycles.  12 . 5  cm.  spheres. 

Points  1000  cycles.) 


bear  this  out.1  High  local  voltages  may  result  from  high  fre- 
quency, oscillations,  etc.  The  flux  may  lag  behind  the  voltage 
in  non-homogeneous  insulations.  (This  does  not  apply  to  air.) 
For  a  given  thickness  of  a  homogeneous  insulation,  and  when 
heating  does  not  result,  a  greater  oscillatory  or  impulse  voltage  of 
short  duration  is  generally  necessary  to  cause  puncture  than  at 
60  cycles. 

Some  of  the  effects  will  now  be  discussed : 

Frequency. — Over  the  commercial  range  there  is  no  variation 
in  sphere-gap  voltages  due  to  frequency.  Figs.  103  and  104  show 
spark-over  curves  up  to  25  kv.  at  1000-cycle  sine  wave  from  an 
alternator.  The  voltage  was  measured  by  a  static  voltmeter 
calibrated  at  60  cycles.  The  drawn  curve  is  tne  60-cycle  cixrve, 
the  points  are  measured  values.  The  d.c.  spark-over  voltage  is 

i  Peek,  "  The  Effect  of  Transient  Voltages  on  Dielectrics,"  A.I.E.E. 
Trans.,  1915,  Vol.  XXXLV,  p.  1857.  See  appendix. 


SPARK-OVER 


107 


, 


t 


generally  equal  to  the  maximum  of  the  60  ~  spark-over  voltage.1 
Fig.  105  gives  a  60-cycle  curve,  and  also  a  40,000-cycle  curve 
from  a  sine  wave  alternator.  The  voltage  in  this  case  was  meas- 
ured by  a  static  voltmeter.  No  special  care  was  taken  to  polish 
the  sphere  surfaces.  At  low  frequencies,  at  rough  places  on  the 
electrode  surface;  there  is  local  overstress;  but  even  if  the  air  is 
broken  down,  the  loss  at  these  places  is  very  small  and  the 
streamers  inappreciable.  At  continuous  high  frequency,  say 

40,000  cycles,  a  local  break- 

down  at  a  rough  point  probably 
takes  place  at  very  nearly  the 
same  gradient  as  at  60  cycles, 
but  the  energy  loss  after  the 
breakdown  at  this  point  oc- 
curs may  be  1000  times  as 
great.  This  forms  a  needle- 
like  streamer  which  increases 
the  stress  and  local  loss. 
Spark-over  then  takes  place 
from  the  " electric  needle"  at 
a  lower  voltage  than  the  true 
sphere-gap  voltage;  thus  it 

seems  that  the  air  at  high  fre- 

/•  ,7       T.  7  i      FIG.  105. — Sphere  gap  spark-over  volt- 

quency  of  the  above  order  is  only    ages  at  60  £ycles  ££  £0j000  cycles, 

apparently    of   less   strength. 

These  " electric  needles"  when  once  formed  may  be  blown  to 
different  parts  of  the  sphere  surface.  The  corona  starting  point 
appears  to  take  place  at  a  lower  voltage  at  high  frequency,  be- 
cause the  local  loss  at  rough  points,  which  occurs  before  the  true 
critical  voltage  is  reached,  is  very  high  at  high  frequency  and 
distorts  the  field  and  masks  the  true  starting  voltage.  The  loss 
at  rough  points  starts  at  the  same  voltage  at  low  frequency  but 
is  inappreciable  and  cannot  change  conditions.  If  the  sphere 
surfaces  are  very  highly  polished  it  seems  that  the  high-frequency 
spark-over  voltage  should  check  closely  with  the  60-cycle  voltage. 
This  should  also  apply  for  corona  on  polished  wires.  The 
following  limitation,  however,  applies  to  both  cases.  At  con- 
tinuous  high  frequency  when  the  rate  of  energy  or  power  is  great, 
frequency  may  enter  into  the  energy  distance  equation  thus 


28 

26 

24 

.22 

'£20 

gl« 

2  16 


0  0.1 0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9 1.0  1.1 1.2  L3, 

Spacing  cm. 


1  See  appendix.     Peek,  The  Effect  of  High  Continuous  Voltages  on  Air, 
Oil  and  Solid  Insulation.     A.I.E.E.,  June,  1916. 


108  DIELECTRIC  PHENOMENA 

and  spark-overs  take  place  at  lower  voltages  at  very  high  fre- 
quency. This  is  more  fully  discussed  in  Chapter  VIII. 
\j  Destruction  of  insulation  by  high  frequency,  when  heating 
does  not  result,  is  due  to  local  overvoltage.  For  instance,  low 
high-frequency  voltage  may  be  applied  to  a  piece  of  apparatus 
containing  inductance  and  capacity,  as  a  transformer.  On  ac- 
count of  the  capacity  and  inductance,  very  high  overvoltage  may 
be  built  up  and  breakdown  result  due  to  overvoltage.  The  petti- 
coat of  an  insulator  may  be  broken  down  by  an  "  electric  needle," 
forming  as  described  above,  bringing  the  total  stress  on  the  thin 
petticoat.  The  sphere  curves  check  very  closely  for  oscillatory 
voltage  of  short  duration  and  voltages  of  steep  wave  front,  even 
under  ordinary  conditions  of  surface.  With  needle  gaps  the 
results  are  quite  different  at  high  and  low  frequency.  At 
continuous  high  frequency  the  needle  point  becomes  hot,  due 
to  the  loss,  and  spark  over  takes  place  at  low  voltage.  For 
impulses,  the  opposite  is  true.  The  sphere  gap  is  thus  the  most 
reliable  means  of  measuring  oscillatory  voltages,  and  voltages  of 
steep  wave  front.  When  used  for  continuous  high  frequency  the 
surfaces  must  be  kept  highly  polished. 

Dielectric  Spark  Lag,  Steep  Wave  Front,  and  Oscillations. — A 
fixed  minimum  voltage  is  required  to  spark  over  a  given  gap 
when  the  time  is  not  limited.  Energy  is  required  to  rupture 
gaseous,  liquid  and  solid  insulations,  this  introduces  a  time  ele- 
ment.1 Thus,  on  account  of  this  time  lag,  when  voltage  is 
applied  at  a  very  rapid  rate  as,  by  an  impulse,  spark-over  does 
not  occur  when  the  continuously  applied  breakdown  voltage  is 
reached.  The  voltage  "over  shoots"  or  rises  above  this  value 
during  the  time  that  the  rupture  is  taking  place.  This  excess 
or  rise  in  voltage  above  the  continuously  applied  breakdown 
value  is  greater  the  greater  the  time  lag  of  the  gap  and  the  rate  of 
application  of  voltage .  Electrodes  having  approximately  uniform 
fields  as  spheres  have  minimum  lag;  needle  gaps  maximum  lag. 

If  the  voltage  required  to  spark  over  a  given  surface  or  gap  is 
measured  at  60  cycles  and  at  steep  wave  front,  it  is  found  that 
the  latter  voltage  is  higher.  The  ratio  of  impulse  spark-over 
voltage  to  the  60-cycle  spark-over  voltage  is  here  termed  the 
"  impulse  ratio."  Spheres  measure  very  closely  the  actual  volt- 
age, even  at  steep  impulses.  Test  results  made  by  the  author 
showing  the  increase  in  voltage  for  the  needle  gap  are  given  in 
Table  XXXV.2  "  The  impulse  used  was  not  steep  enough  to 

1  See  page  198. 

2  Peek,  "  Effect  of  Transient  Voltages  on  Dielectrics,"  A.I.E.E.  Trans., 
1915,  Vol.  XXXLV,  p.  1857.     "  Lightning,"  G.  E.  Review,  July,  1916.     See 
appendix. 


SPARK-OVER 


109 


TABLE  XXXV. — IMPULSE  RATIO  OF  NEEDLE  GAP 


Spacing  of  needles 
(cm.) 

Voltage  required  to  cause  needle  gap  to 
spark  over 

Ratio  impulse  to 
60  cycles, 
voltage 

60  cycles  (max.) 

Impulse  measured  by 
25-cm.   spheres    (dia.) 
(max.) 

4.3 

8.0 
12.0 
25.0 

43.1 

64.8 
85.0 
134.0 

62.0 
96.1 
140.0 
260.0 

1.45 

1.49 
1.65 
1.94 

TABLE  XXXVI. — IMPULSE  RATIO  OF  6.25-CM.  SPHERE 
(Compared  to  25-cm.  Sphere) 


6.25-cm.   diameter 
sphere  gap,  cm. 

Voltage  required  to  cause  6.25-cm.  sphere  to 
spark  over  at  gaps  greater  than  the  diameter 

Ratio    impulse  to 
60  cycles, 
voltage 

60  cycles  (max.) 

Impulse  measured  by 
25-cm.  sphere  (dia.) 
(max.) 

6 

127 

134 

.05 

8 

144 

152 

.05 

9 

154 

160 

.04 

10 

156 

168 

.06 

12 

168 

180 

.08 

15 

180 

198 

.10 

appreciably  affect  the  sphere.  Note  the  very  high  impulse  volt- 
age required  to  spark  over  a  needle  gap  compared  to  the  60-cycle 
spark-over  voltage.  This  indicates  that  the  needle  gap  is  very 
slow.  Corona  produced  by  transient  voltages  can  be  seen  and 
the  eye  can  distinguish  between  a  positive  and  negative  wire 
when  volcages  producing  the  corona  last  less  than  a  micro  second. 
Care  must  be  taken  when  measuring  the  spark  voltage  on  one 
gap  by  another  gap  in  parallel ;  for  instance,  if  a  needle  gap  is  set  so 
as  to  just  spark  over  when  voltages  of  steep  wave  front  or  high 
frequency  oscillation  of  a  given  value  are  applied,  and  a  sphere  gap 
is  similarly  set,  and  these  two  gaps  are  then  placed  in  parallel, 
and  the  same  impulse  voltage  applied,  apparent  discrepancy  re- 
sults. Spark-over  will  take  place  across  one  gap  and  not  the 
other,  even  when  the  spacing  on  the  non-sparking  gap  is  decreased. 
This  will  be  noticed  in  all  cases  where  electrodes  of  different  shapes 
are  placed  in  parallel.  When  the  impulse  voltage  is  applied 
across  the  "fast"  gap  and  the  "slow"  gap  in  multiple,  the  "fast" 
gap  will  spark  over,  relieving  the  stress,  before  the  "slow"  gap 


110 


DIELECTRIC  PHENOMENA 


has  time  to  act,  even  though  the  slow  gap  is  set  for  a  much  lower 
voltage.  The  difference  would  not  be  apparent  at  commercial 
frequencies. 

TABLE  XXXVII. — IMPULSE  RATIO  OF  NEEDLE  GAP 
(Impulse  Circuit,  Fig.  106) 


Voltage  required  to  cause  needle  gap  to  spark  over 

Spacing  of 
needle  (cm.) 

60  cycles 
(max.) 

Impulse  measured 
by  25-cm.  spheres 
(max.) 

Impulse  calculated 
from    circuit   con- 
stants (max.) 

Ratio  impulse 
to  60  cycles, 
voltage 

2.30 

27 

32.5 

32.5 

1.20 

3.19 

35 

45.5 

46.0 

1.30 

3.95 

41 

55.0 

56.0 

1.35 

4.44 

45 

65.0 

64.0 

1.40 

5.34 

50 

73.0 

74.0 

1.45 

10.00 

76 

133.0 

135.0 

1.75 

100 


Imp   IseVol 


An  example  of  the  impulse  used  by  the  author  to  obtain  the 
data  in  Table  XXXVII  is  shown  in  Fig.  106. 1     It  reaches  its 

maximum  in  5  X  10~7  seconds 
and  approximates  a  single  half 
cycle  of  a  500,000-cycle  wave. 
The  calculated  values  of  these 
voltages  check  approximately 
with  those  measured  by  the 
spheres.  It  thus  appears  that 
the  sphere  voltages  are  very 
little  affected,  even  at  this 
steep  impulse. 


60 


40 


0.2     0.4       0.6       0.8 
Time-Micro-Seconds 


1.2 


FIG. 


106. — Impulse  voltage  and  cir- 
cuit producing  it.2 


The  needle  requires  the  maxi- 
mum time  of  any  gap  as  con- 
siderable air  must  be  "  ionized  " 
before  spark-over  can  result. 

The  spheres  are  very  little  affected  because  corona  does  not 
precede  spark-over,  and  the  discharge  is  small  and  confined  to  a 
short  path.  The  field  is  very  nearly  regular  and  rupture  starts 
everywhere  along  the  path  between  the  electrodes  at  approxi- 
mately the  same  time. 

The  line  insulator  is  generally  designed  so  that  at  commercial 

1  Impulse  takes  place  at  I  due  to  discharge  of  condenser  C,  through  R,  L, 
and  power  arc  at  A.     (See  page  162.) 

2  One  micro-second  =one  millionth  of  a  second. 


SPARK-OVER  111 

frequencies  the  spark-over  voltage  is  lo\ver  than  the  puncture 
voltage.  For  lightning  or  impulse  both  the  spark-over  voltage 
and  the  puncture  voltage  should  be  much  higher.1  By  applying 
a  sufficient  number  of  impulses  at  voltages  higher  than  the 
60-cycle  puncture  voltage,  an  improperly  designed  insulator 
may  be  punctured.  During  the  time  that  the  air  is  breaking 
down,  this  overstress  produces  small  cracks  in  the  porcelain. 
The  effect  is  cumulative.  The  cracks  gradually  extend  and 
puncture  results.  This  subject  is,  hence,  of  great  importance. 
In  making  spark  measurements  it  is  necessary  to  consider  the 
spark  lag,  as  otherwise  totally  erroneous  conclusions  may  be 
reached.  It  is  therefore  necessary  in  making  spark-over  measure- 
ments on  certain  apparatus  to  guard  against  this.  For  instance, 
on  line  insulators  there  is  generally  considerable  corona  discharge 
long  before  spark-over.  This  discharge  may  cause  oscillation 
which  will  affect  the  measuring  gap  and  cause  a  lower  voltage 
to  arc  over  given  distances  than  normal,  or  cause  the  gap  to 
cause  higher  voltages  than  really  exist.  This  is  eliminated  in 
practice  by  the  use  of  high  resistance  in  the  measuring  gap. 

One  investigation  of  impulse  voltages,  indicating  that  time 
and  energy  are  necessary  to  rupture  insulation,2  shows  that 
"the  disruptive  discharge  through  a  dielectric  requires  not  merely 
a  sufficiently  high  voltage,  but  requires  a  definite  minimum 
amount  of  energy. 

"The  disruptive  discharge  does  not  occur  instantly  with  the 
application,  but  a  finite,  though  usually  very  small,  time  elapses 
after  the  application  of  the  voltage  before  the  discharge  occurs. 
During  this  time  the  disruptive  energy  is  supplied  to  the  dielectric." 

The  disruptive  energy  of  oil  seems  to  be  about  30  times  greater 
than  it  is  for  air.  This  is  further  discussed  in  Chapter  VI. 

Effect  of  Altitude  on  the  Spark-over  Voltages  of  Bushings, 
Leads,  and  Insulators. — For  non-uniform  fields,  as  those  around 
wires,  spheres,  insulators,  etc.,  the  spark-over  voltage  decreases 
at  a  lesser  rate  than  the  air  density.  The  theoretical  reasons  for 
this  have  been  given,  as  well  as  the  laws  for  regular  symmetrical 
electrodes,  for  cylinders  and  spheres. 

It  is,  however,  not  possible  to  give  an  exact  Taw  covering  all 
types  of  leads,  insulators,  etc.,  as  every  part  of  the  surface  has  its 
effect.  The  following  curves  and  tables  give  the  actual  test 
results  on  leads,  insulators  and  bushings  of  the  standard  types. 
The  correction  factor  for  any  other  lead  or  insulator  of  the  same 

1  See  data,  appendix. 

2  Hayden  and  Steinmetz,  A.I.E.E.,  June,  1910. 


112 


DIELECTRIC  PHENOMENA 


type  may  be  estimated  with  sufficient  accuracy.  When  there  is 
doubt  6  may  be  taken  as  the  maximum  correction.  It  will  gen- 
erally be  advisable  to  take  5  because  the  local  corona  point  on 
leads  and  insulators  will  vary  directly  with  5.  This  is  so  because 
the  corona  must  always  start  on  an  insulator  in  a  field  which  is 
locally  more  or  less  uniform. 

The  tests  were  made  by  placing  the  leads  or  insulators  in  the 
large  wooden  cask,  already  referred  to,  exhausting  the  air  to 
approximately  8  =  0.5,  gradually  admitting  air  and  taking  the 
spark-over  voltage  at  various  densities  as  the  air  pressure  in- 
creased. The  temperature  was  always  read  and  varied  between 
16  and  25  deg.  C. 

At  the  start  a  number  of  tests  were  made  to  see  if  a  spark-over 
in  the  cask  had  any  effect  upon  the  following  spark-overs  by 
ionization  or  otherwise.  It  was  found  that  a  number  of  spark- 
overs  could  be  made  in  the  cask  with  no  appreciable  effect. 
During  the  test,  the  air  was  always  dry  and  the  surfaces  of  the  v 
insulators  were  kept  clean. 

TABLE  XXXVIII. — SUSPENSION  INSULATOR 


Bar.  cm. 

Vac.  cm. 

Pressure 

Temp, 
cent. 

1 

Kilovolts 
arc-over 

75.4 

37.4     , 

38.0 

22.0 

0.50 

121.0 

75.4 

34.3 

41.1 

22.0 

0.54 

131.0 

75.4 

30.0 

45.4 

22.0 

0.60 

144.0 

75.4 

26.4 

49.0 

22.0 

0.65 

158.5 

75.4 

23.0 

52.4 

22.0 

0.70 

165.0 

75.4 

19.3 

56.0 

22.0 

0.74 

177.5 

75.4 

17.5 

57.9 

22.0 

0.87 

183.2 

75.4 

15.0 

60.4 

22.0 

0.80 

195.0 

TABLE  XXXIX. — LEADS 
Correction  Factor  for  Leads  Shown  in  Fig.  107 


1 

(«) 

<&) 

(c) 

(d) 

1.00 

1.00 

1.00 

1.00 

1.00 

0.90 

0.92 

0.91 

0.92 

0.92 

0.80 

0.83 

0.82 

0.83 

0.85 

0.70 

0.74 

0.72 

0.75 

0.77 

0.60 

0.70 

0.65 

0.64 

0.66 

0.50 

0.61 

0.56 

0.54 

0.57 

SPARK-OVER 


113 


TABLE  XL. — POST  AND  PIN  INSULATORS 
Correction  Factor  for  Insulators  Shown  in  Fig.  108 


(a) 

(b) 

(c) 

Post 

Pin 

1.00 

1.00 

1.00 

1.00 

0.90 

0.93 

0.91 

0.94 

0.80 

0.84 

0.81 

0.86 

0.70 

0.76 

0.72 

0.75 

0.60 

0.68 

0.62 

0.65 

0.50 

0.60 

0.52 

0.53 

TABLE  XLL — SUSPENSION  INSULATOR 

Fig.  109 
Correction  Factor  for  Units  in  String  as  Follows 


Number  of  units 


s 

l 

2 

3 

4 

5 

1.00 
0  90 

1.00 
0  96 

1.00 
0  93 

1.00 
0  90 

1.00 

1.00 

0.80 

0.91 

0.84 

0.80 

0  70 

0  86 

0  76 

0  70 

0.60 

0.80 

0.66 

0.60 

0.50 

0  72 

0  55 

0  50 

TABLE  XLII. — SUSPENSION  INSULATOR 

Fig.  110 
Correction  Factor  for  Units  in  String  as  Follows 


Number  of  units 


S 

1 

2 

3 

4 

5 

1.00 
0.90 

1.00 
0  94 

1.00 
0  92 

1.00 
0  90 

1.00 
0  90 

1.00 

0  80 

0  87 

0  84 

0  80 

0  80 

0.70 

0.81 

0.73 

0  70 

0  70 

0.60 

0.72 

0  63 

0  60 

0  60 

0.50 

0.62 

0.52 

0.50 

0.50 

Table  XXXVIII  is  a  typical  data  sheet.  Tables  XXXIX- 
XLI  give  even  values  of  8  and  the  corresponding  measured  cor- 
rection factors.  If  the  spark-over  voltage  is  known  at  sea  level 
or  5  =  1(76  cm.  bar.,  temperature  25  deg.  C.),  the  spark-over 


114 


DIELECTRIC  PHENOMENA 


.1  .2  .3  .4  .5  .6  .7  .8  .9  1.0 1.1 

Belatiue    Density 

FIG.  107. — Variation  of  spark- 
over  voltage  of  transformer  leads 
with  air  density. 

(a)   15.2  cm.  high  by  17.8  cm.  dia. 

(6)  21.6  cm.  high  by  17.8  cm.  dia. 

(c)  28  cm.  high  by  17.8  cm.  dia 

(d]  38.1  cm.  high  by  17.8  cm.  dia. 

Height  measured  from  case  to  metal  cap  on  top. 


150 
140 
130 
120 
110 
100 
90 
80 
70 
60 
50 
40 
30 
20 
10 
0 

1 

c  J    \ 

!•» 

^ 

^ 

C 

4 

? 

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.1  .2  .3   .4   .5  .6   .7  .8  .9    1.01.1 

Kelative    Densities 

FIG.  108. — Variation  of  spark-over 
voltage  insulators  with  air  density. 

(a)  30.2  cm.  high. 

(6)   13. 5  cm.  high  by  16.8cm.  dia. 

(c)  28.6  cm  high  by  36  cm.  dia. 


Z1U 

200 
190 
180 
170 
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Arc  Over  Voltages 
at 
Various  Air  Densities 

.1     .2    .3    .4    .5    .6    .7    .8    .9   1. 

210 
200 
190 
180 
170 
160 
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Arc  Over  Voltages 
at 
Various  Air  Densities 

Relative  Density 

FIG.  109. — Suspension  insulator. 
(Dia.,  30  cm.    Spacing  16.5  cm.) 


.1    .2    .3    .4    .5    .6   .7    .8    .9    1.0 
Relative  Density 

FIG.  110. — Suspension  insulator. 
(Dia.,  27cm.    Spacing  17  cm.) 


SPARK-OVER 


115 


at  any  other  value  of  6  may  be  found  by  multiplying  by  the  cor- 
responding correction  factor.  It  will  be  noted  that  in  most  cases 
the  correction  factors  are  very  nearly  equal  to  5.  6  would  be 
the  correction  factor  in  a  uniform  field  and  should  be,  as  already 
stated,  taken  as  such  in  most  cases,  especially  where  dirt  and 
moisture  enter,  as  in  practice.  Furthermore,  it  should  be  taken 


15000 
14000 
13000 
12000 
11000 
10000 
9000 
8000 
7000 
6000 
5000 
4000 
3000 
2000 
1000 

\ 

V 

\ 

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.5 


.6  .7  .8 

5   Relative  Air  Density 


1.0 


FIG.   111. — Approximate  variation  of  air  density  with  altitude. 

as  it  is  the  actual  correction  factor  for  the  starting  point  of  local 
corona  on  insulators. 

Fig.  Ill  is  a  curve  giving  different  altitudes  and  corresponding 
5  at  25  deg.  C.  If  the  spark-over  voltage  is  known  at  sea  level 
at  25  deg.  C.,  the  spark-over  voltage  at  any  other  altitude  may 
be  estimated  by  multiplying  by  the  corresponding  5,  or  more 
closely  if  the  design  is  the  same  as  any  in  the  tables,  by  the  cor- 
rection factor  corresponding  to  5.  If  the  local  corona  starting 
point  is  known  at  sea  level,  it  may  be  found  for  any  altitude  by 
multiplying  by  the  corresponding  <5.  If  the  barometric  pressure 
and  temperature  are  known,  5  may  be  calculated. 


116  DIELECTRIC  PHENOMENA 

As  an  example  of  the  method  of  making  corrections:  Assume 
a  suspension  insulator  string  of  three  units  with  a  spark-over 
voltage  of  205  kv.  (at  sea  level  25  deg.  C.  temperature).  5  =  1. 
What  is  the  spark-over  voltage  at  9000  ft.  elevation  and  25 
deg.  C.? 

From  Fig.  Ill,  the  5  corresponding  to  9000  ft. 

d  =  0.71 

Then  the  approximate  spark-over  voltage  at  9000  ft.v  25  deg.  C. 
is 

ei  =  0.71  X  205  =  145  kv. 

If  this  happens  to  be  the  insulator  of  Fig.  110,  the  correction 
factor  corresponding  to  d  =  0.71  is  found  in  Table  XLII,  by  inter- 
polation to  be  0.71.  The  actual  spark-over  voltage  for  the  special 
case  happens  to  check  exactly  with  that  given  by  5.  For  prac- 
tical work  a  correction  may  generally  be  made  directly  by  use  of 
Fig.  111. 

.  The  spark-over  voltage  of  an  insulator  is  100  kv.  at  70  cm. 
barometer  and  20  deg.  C.  What  is  the  approximate  spark-over 
voltage  at  50  cm.  barometer  and  10  deg.  C.? 

_3.92^70_. 
81  "  -273"+  30   ' 

3.92  X  50 
52  =:   273  +  10   : 


If  the  local  corona  starting  point  is  known  at  sea  level,  it  may 
be  found  very  closely  for  any  other  altitude  by  multiplying  by 
the  correction  6. 

Wet  Spark-over  of  Insulators  and  Bushings.  —  The  wet  or  rain 
60  ~  spark-over  voltage  is  generally  from  50  to  90  per  cent,  of  the 
dry  spark-over  voltage.  The  lower  figure  applies  to  smooth  bush- 
ings, the  higher  figure  to  corrugated  bushings.  The  altitude 
correction  is  made  on  the  wet  in  the  same  way  as  on  the  dry 
spark-over. 

The  lightning  or  impulse  spark-over  voltage  is  generally  not 
lowered  by  rain.1 

1  Peek,  "  Factors  Determining  the  Safe  Spark-over  Voltage  of  Insulators 
and  Bushings  for  High  Voltage  Transmission  Lines,"  G.  E.  Rev.,  June, 
1916.  (See  appendix.) 


CHAPTER  V 


CORONA  LOSS 

In  the  present  chapter  the  corona  loss  is  discussed.  It  has 
been  thought  worth  while  to  go  into  details  in  the  description  of 
the  apparatus,  methods  of  making  loss  tests,  and  reducing  data1 
as  an  example  of  an  extremely  large  engineering  investigation. 
Experimentally,  the  methods  followed  apply  to  any  investigation; 
practically,  many  of  the  detailed  observations  have  an  important 
bearing;  theoretically  and  experimentally  the  observed  details 
are  of  importance  and  the  methods  of  reducing  data  may  be 
applied  to  other  investigations. 

Lines,  Apparatus  and  Method  of  Test. — The  Lines.  The  first 
investigation  was  made  out  of  doors.  The  conductors  used  in 

North 


Variable 

KX 

n  nun               Conductor 

HIIIII 

10'2"  i 

T" 

IHHH  ^« 

»  ! 

t    102"               _""_ 

? 

«  /\  X 

102'  T 

i 

HWf>r1 

. Insulators 


South 


Corona  Loss 
Final  Line  Arrangement 

Line  A  Standard  Line 
.465"Diam.  7  Str.  Cable 

Line  B  Variable  Line 


.* -417  'll" 


FIG.  112. — Experimental  outdoor  line. 

this  investigation  were  supported  by  metal  towers  arranged  in  two 
parallel  lines  of  two  spans  each.     The  length  of  each  span  was 
approximately  0. 150  km.     These  tower  lines  will  be  designated  by 
A  and  B  respectively.     The  conductors  were  strung  in  a  hori- 
zontal plane  with  seven  disk  suspension  insulators  at  each  point 
*Law  of  Corona,  A.  I.  E.  E.,  June,  1911. 
8  H7 


118 


DIELECTRIC  PHENOMENA 


of  support.  For  preliminary  tests  four  No.  3/0  B.  &  S.  (1.18  cm. 
diameter)  seven-strand,  hard-drawn  copper  cables  were  put  in 
place  on  each  line.  A  seven-strand  steel  ground  cable  was  also 
strung.  After  a  number  of  tests  had  been  made  the  ground  cables 
were  removed  from  line  A.  The  conductors  on  line  A,  however, 
were  kept  in  place  as  a  standard  throughout  all  the  investigations. 
The  conductors  were  removed  from  B,  and  the  first  span  of  this 
line  was  used  to  support  various  sizes  of  conductors  at  various 
spaces.  (See  Fig.  112.) 

These  lines  were  erected  in  a  large  field.  The  prevailing  winds 
were  from  the  west  over  open  country,  that  is,  free  from  smoke 
from  the  city  and  the  factory  on  the  east. 

Test  Apparatus. — A  railroad  track  was  run  directly  under  the 
line,  and  the  testing  apparatus  was  housed  in  three  box  cars. 


120 

100 

4, 

80 
60 
40 
20 
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20 
40 
60 
80 
100 
120 

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1-  Fundamental  Voltage  Wave 
2  -  Original  Voltage  Wave 
3  -  3rd  Harmonic  Voltage 
4-  Fundamental  Current 
5-  Original  Current 
6-  3rd  Harmonic  Current 

V 

^ 

, 

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X 

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s 

JN- 

^ 

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FIG.  113. — Analysis  of  applied  voltage  and  corona  current  wave. 

This  proved  a  very  convenient  arrangement,  as  the  cars  could  be 
quickly  run  back  to  the  factory  when  changes  or  repairs  were 
necessary. 

Power  was  supplied  from  an  old  Thomson-Houston  machine 
with  a  smooth  core,  pan  cake  winding  on  the  armature;  it  gave  a 
very  good  wave,  and  was  used  in  all  tests.  See  oscillogram  and 
analyzed  wave,  Fig.  113.  It  was  rated  at  35  kw.,  but  this  rating 
was  quite  conservative.  This  alternator  was  belted  to  a  d.c. 
motor. 

The  high  voltage  transformer  and  the  testing  apparatus  were 
placed  in  car  No.  2.  The  portion  of  the  car  roof  over  the  trans- 


CORONA  LOSS 


119 


former  was  made  of  heavy  canvas.  This  could  be  quickly  rolled 
back,  and  the  leads  from  the  line  were  dropped  directly  to  the 
transformer  terminal.  By  means  of  a  framework  and  canvas 
cover  the  transformer  could  be  protected  from  the  weather,  and 
investigations  carried  on  during  rain  and  snow  storms.  The 
power  supply,  speed  and  voltage,  were  all  controlled  from  car  No. 
2.  In  fact  all  of  the  adjustments  could  be  made  from  this  car 
(see  Fig.  114).  The  transformer  was  rated  at  100  kw.,  200,000 
volts  and  60  cycles.  On  the  low  side  were  four  500  volt  coils. 
These  coils  could  be  connected  in  multiple  or  series  for  change  of 
ratio.  The  high  tension  winding  was  opened  at  the  neutral  and 
taps  were  brought  out  for  the  ammeter,  and  current  coil  of  the 
wattmeter.  Three  taps  were  also  brought  out  here  from  the 
main  winding  for  voltage  measurement.  (See  Fig.  114.)  The 
following  tap  ratios  were  thus  obtained :  100/200,000;  200/200,000 
and  400/200,000. 


Eotary 


Carl 


Car  II 


FIG.  114. — Circuit  connections  in  corona  loss  measurements. 

Car  No.  3  served  as  a  dark  room  for  making  photographs  and 
visual  tests  on  short  wires  and  cables. 

Methods  of  Test. — Accurate  power  measurements  of  corona  are 
difficult  to  make,  because  of  the  nature  of  the  load,  low  power 
factor  and  high  voltage.  It  is  not  desirable  to  make  the  measure- 
ments on  the  low  side  because  of  the  difficulty  in  separating  the 
transformer  iron  and  load  losses,  and  these  may  be  sometimes  as 
large  as  the  corona  losses.  In  these  tests  the  current  coil  of 
the  wattmeter  and  the  ammeter,  were  put  in  the  high  tension 
winding  of  the  transformer  at  the  neutral  point,  and  the  neutral 
was  grounded.  The  voltage  coil  of  the  wattmeter  was  connected 
to  a  few  turns  of  the  high  tension  winding  at  the  neutral.1  All 
of  the  loss  measurements  were  also  duplicated  on  the  low  side  as  a 

1A.  B.  Hendricks,  A.  I.  E.  E.  Transactions,  Feb.,  1911. 


120  DIELECTRIC  PHENOMENA 

TABLE  XLIII. — EXPERIMENTAL  LINE — A.     CORONA  Loss — 10-6-10.    4  P.M. 


Low  side  total  readings 

High  side  total  readings 

Volts 

Amperes 

Kilowatts 

Kilovolts 

Amperes 

Kilowatts 

Line  on 

395 

16.5 

0.40 

80.5 

0.077 

0.10 

435 

17.9 

0.60 

90.5 

0.087 

0.13 

490 

20.5 

0.70 

101.6 

0.101 

0.17 

535 

22.6 

0.80 

111.1 

0.112 

0.22 

590 

24.7 

1.00 

120.4 

0.119 

0.28 

635 

27.1 

1.10 

130.2 

0.135 

0.35 

'  680 

29.2 

1.40 

139.2 

0.145 

0.45 

735 

31.6 

1.80 

150.0 

0.158 

0.68 

780 

33.4 

2.40 

159.0 

0.169 

1.10 

812 

35.3 

3.30 

165.8 

0.178 

1.80 

830 

36.3 

3.60 

169.0 

0.181 

2.40 

862 

37.5 

5.12 

176.6 

0.190 

3.60 

893 

39.2 

6.35 

183.2 

0.199 

4.70 

914 

40.5 

7.50 

187.0 

0.207 

6.00 

975 

43.9 

11.40 

200.0 

0.227 

9.30 

1020 

47.8 

14.50 

209.0 

0.243 

12.60 

1050 

49.3 

17.00 

214.2 

0.253 

14.60 

1080 

52.7 

19.50 

220.2 

0.267 

17.60 

1125 

55.5 

22.80 

223.4 

0.283 

20.30 

Line  off 

400 

1.14 

0.40 

80.0 

0.005 

0.05 

500 

1.37 

0.62 

100.5 

0.007 

0.10 

600 

1.63 

0.82 

121.5 

0.008 

0.15 

718 

1.87 

1.18 

143.5 

0.010 

0.21 

812 

2.05 

1.45 

161.0 

0.011 

0.28 

905 

2.29 

1.80 

181.0 

0.013 

0.35 

1015 

2.69 

2.20 

202.2 

0.015 

0.44 

1095 

3.25 

3.64 

217.0 

0.017 

0.54 

Cloudy-rain  in  morning. 
C.,  dry  12  deg.  C. 


Weather 
Barometer  75  cm.  Temperature:  wet   10  deg. 

Line  and  connections 


(1  and  3)  (2  and  4)  ground  wires  in  place. 

Total  conductor  length 109,500  cm. 

Spacing 310  cm. 

No.  3/0  seven-strand  cable  diameter 1.18  cm. 

Transformer  ratio 1000/200,000 

Frequency 60  cycles. 


CORONA  LOSS  121 

check.  Frequency  was  held  at  the  test  table  by  means  of  the 
motor  field  and  a  vibrating  reed  type  of  frequency  meter. 

Voltage  was  controlled  in  two  ways — by  the  potentiometer 
method  and  by  rheostats  in  the  alternator  field.  By  the  potenti- 
ometer method  is  meant  a  resistance  in  series  with  the  supply  on 
the  low  side  of  the  transformer  for  voltage  control  and  a  multiple 
resistance  across  the  transformer,  taking  about  three  times  the 
exciting  current,  to  prevent  wave  distortion.  When  the  leading 
current  was  very  high  a  reactance  was  arranged  to  shunt  the 
generator  and  approximately  unity  power  factor  could  be  held. 
This  prevented  overloading  the  generator  and  reduced  wave  shape 
distortion.  For  a  set  of  tests  at  a  given  frequency  the  ratio  of 
the  main  transformer  was  kept  the  same.  Where  losses  at  several 
frequencies  were  to  be  compared  the  main  transformer  ratio  also 
was  changed  to  keep  the  flux  on  the  generator  as  nearly  constant 
as  possible — for  instance,  at  45  cycles  a  ratio  of  500/200,000 
would  be  used,  while  at  90  cycles  a  ratio  of  1000  to  200,000  would 
be  used.  Wattmeters  especially  adapted  to  the  tests  were  con- 
structed. These  were  of  the  dynamometer  type;  each  was  pro- 
vided with  a  75-volt  and  150-volt  tap.  The  voltmeter  coil  ratio 
on  the  transformer  and  the  wattmeter  tap  were  always  changed 
to  give  the  best  reading.  Four  wattmeters  were  used  in  these 
tests.  The  meters  were  all  carefully  calibrated  in  the  laboratory 
at  unity  power  factor  and  at  0.10  leading  power  factor,  at  both 
25  and  60  cycles. 

Humidity,  temperature  and  barometric  pressures,  as  well  as 
general  weather  observations,  were  taken  during  each  test. 

Indoor  Line. — Later  an  extensive  investigation  was  made  in  a 
large  laboratory  room,  17  meters  wide  by  21  meters  long.  The 
lines  were  strung  diagonally  between  movable  wooden  towers. 
Strips  of  treated  wood  1.25  cm.  square  by  80  cm.  long  were  used 
as  insulators.  The  total  length  of  conductor  possible  with  four 
wires  was  80  meters.  By  this  arrangement  it  was  possible  to 
make  a  more  complete  study  on  the  smaller  sizes  of  conductors, 
and  also  to  extend  the  investigation  over  a  greater  frequency 
range.  The  apparatus  used  was  otherwise  the  same  as  in  the 
outdoor  tests. 

The  Quadratic  Law. — Table  XLIII  is  a  typical  data  sheet  for 
Line  A.  Fig.  115  and  Fig.  118  show  the  characteristic  corona 
curves.  The  corrected  values  for  Table  XLIII  are  recorded  in 
Table  XLIV. 


122 


DIELECTRIC  PHENOMENA 


TABLE  XLIV. — CORONA  Loss,  OBSERVED  VALUES  CORRECTED  FROM 
TABLE  XLIII 


Kilovolts 
between 
lines  ** 

Line  ampere 

Kilovolts 
to  neutral  e 

Kilowatts 
line  loss  p 

K.v.a. 

Power  factor 

80.5 

0.072 

40.2 

5.80 

90.5 

0.081 

45.2 

7.33 

101.6 

0.094 

50.8 

9.55 

111.1 

0.104 

55.5 

11  55 

120.4 

0.111 

60.2 

0.11 

13.40 

0.008 

130.2 

0.126 

65.1 

0.15 

16.40 

0.009 

139.2 

0.135 

69.6 

0.22 

18.80 

0.012 

150.0 

0.147 

75.0 

0.40 

22.10 

0.018 

159.0 

0.157 

79.5 

0.79 

25.00 

0.032 

165.8 

0.166 

82.9 

1.42 

27.60 

0.051 

169.0 

0.168 

84.5 

2.04 

28.40 

0.072 

176.6 

0.177 

88.3 

3.21 

31.20 

0.103 

183.2 

0.185 

91.6 

4.28 

33.90 

0.126 

187.0 

0.193 

93.5 

5.55 

36.10 

0.154 

200.0 

0.212 

100.0 

8.78 

42.40 

0.207 

209.0 

0.227 

104.5 

12  .  02 

47.50 

0.253 

214.2 

0.237 

107.1 

13.99 

50.70 

0.276 

220.2 

0.250 

110.1 

16.94 

55.10 

0.307 

The  shape  of  the  curve  between  kilovolts  and  kilowatts  sug- 
gests a  parabola.  After  trial  it  was  found  that  the  losses  above 
the  knee  of  the  curve  follow  a  quadratic  law.  Below  the  knee  it 
was  found  that  the  curve  deviates  from  the  quadratic  law.  This 
variation  near  the  critical  voltage  is  due  to  dirt  spots,  irregular- 
ities and  other  causes  as  discussed  later.  The  main  part  of  the 
curve  may  be  expressed  by1 


p  =  c2(e  —  e0)' 


(32) 


where 


=  the  line  loss. 

=  kilovolts  to  neutral. 

is  called  the  disruptive  critical  voltage,  measured  in 

kilovolts  to  neutral. 


The  meaning  of  e0  and  c2  will  be  considered  later.  The  best 
mechanism  of  evaluation  of  constants  for  a  given  set  of  tests  may 
now  be  considered.  Equation  (32)  may  be  written 

Vp  =  c(e  -  e0) 
'F.  W.  Peek,  Jr.,  Law  of  Corona,  A.  I.  E.  E.,  June,  1911. 


CORONA  LOSS 


123 


then  if  the  quadratic  law  holds,  the  curve  between  \/p  and  e  will 
be  a  straight  line.  e0  will  be  the  point  where  the  line  cuts  the  e 
axis,  and  c  will  be  the  slope  of  the  line  (see  Fig.  116);  e0  and  c 
may  be  evaluated  graphically  in  this  way.  It  is  difficult  to 
know  how  to  draw  the  line  accurately  and  give  each  point  the 
proper  weight.  To  do  this  the  SA  method  is  used,  as  follows:1 


e0 


ev 


t 


0  110  120  130  140  150  160  170  180  190  200  210 

Between  Lines 

55          65         75          85         95         105 
Kilo-  Volts  (Eff.)         To  Neutral 

FIG.  115.  —  Characteristic  corona  loss  curve  for  large  stranded 

conductor. 

Line  A  conductors  1-2-3-4.  3/0,  7-strand  cable,  diameter,  1.18  cm. 
Total  conductor  length,  109,500  cm.  .  Spacing,  310  cm.  Points,  measured 
values.  Curve  calculated  from  p  =  0.0117  (e—  72.  2)2.  e0  =  Disruptive 
critical  voltage.  ev  =  Visual  critical  voltage.  Test  table  XLIV. 


The  values  of  e  and  p  for  the  set  of  readings  to  be  investigated 
are  first  tabulated  and  a  curve  plotted  (Fig.  1  16)  .  All  points  that 
differ  greatly  from  the  straight  line  are  eliminated  as  probably  in 
error,  or,  as  at  the  lower  part  of  the  curve,  following  a  different 
law.  The  remaining  readings  are  taken  and  formed  into  two 
groups,  each  of  an  equal  number  of  readings. 


Group  1.     Sie 

Group  2.     22e         S2  Vp 

1  Steinmetz,  Engineering  Mathematics,  page  232. 


124 
Then 


DIELECTRIC  PHENOMENA 


_ 


e0 


n 


where  n  is  the  number  of  points  used. 
Thus  e0  and  c  are  determined. 


/ 

I' 

/ 

1 

9 

3 

J 

/ 

C" 

a 

3 

/ 

of 

0 

/ 

P 

</ 

t> 

/ 

!? 

/ 

*& 

•^ 

1fS 

<'/ 

?*, 

3\>*\ 
_--< 

>"M 

1 

1 

110  120  130  140J150  ICO  170  180  190  200  210  Bet.  Lines 
55         65    eo75         85         95        105  To  Neutral 
Kilovolts  Effective 

FIG.  1 16. — Corona  loss  curve  plotted  between  \/p  and  e.     (Large  conductor. 
Data  same  as  Fig.  115.) 

TABLE  XLV. — CORONA  Loss,  CALCULATED  VALUES  FOR  FIG.  115. 

p  =  c\e  -  60)2 

p  =  0.0117  (e  -  72.2)* 


Kilovolts   be- 
tween lines  e' 

Kilovolts  to 
neutral  e 

Kilowatts 
p  =  C2(e-e0)2 

Kilovolts  be- 
tween lines  e' 

Kilovolts  to 
neutral  e 

Kilowatts 
p  =  C2(e-e0)z 

144.4 

72.2 

0.0 

183.2 

91.6 

4.41 

150.0 

75.0 

0.10 

187.0 

93.5 

5.32 

159.0 

79.5 

0.63 

200.0 

100.0 

9.03 

165.8 

82.9 

1.34 

209.0 

104.5 

12.25 

169.0 

84.5 

1.77 

214.2 

107.1 

14.25 

176.6 

88.3 

3.04 

220.2 

110.1 

16.80 

CORONA  LOSS 


125 


TABLE  XLVI. — CORONA  Loss 
Method  of  Reducing  (Data  from  Table  XLIV) 


Kilovolts  between 
line  e' 

Kilovolts  to 
neutral  e 

Kw.,  p 

VP 

120.4 

60.2 

0.11 

0.332 

130.2 

65.1 

0.15 

0.388 

139.2 

69.6 

0.22 

0.470 

150.0 

75.0 

0.40 

0.632 

159.0 

79.5 

0.79 

0.889 

165.8 

82.9 

1.42 

1.192 

169.0 

84.5 

2.04 

1.428 

176.6 

88.3 

3.21 

1.792 

183.2 

91.6 

4.28 

2.069 

187.0 

93.5 

5.55 

2.356 

200.0 

100.0 

8.78 

2.963 

209.0 

104.5 

12.02 

3.467 

214.2 

107.1 

13.99 

3.740 

220.2 

110.1 

16.94 

4.116 

Total  conductor  length 109,500  cm. 

Spacing 310  cm. 

No.  3/0  seven-strand  cable  diameter 1.18  cm. 


91.6       2.069 

93.5       2.356 

100.0       2.963 


104.2  3.467 
107 . 1  3 . 740 
110.1  4.116 


22e  =  285.1 
Zie  =  321.4 


ASe 


36.6 


=  606.8 


AS\/P  =    3.935 


=     7.388 

Si\/P  =   11.323 
e0  =  72.1 
e0'  =144.2 


=  18.711 


c  = 


ASe 


=  0.108 
2  =  0.0115 


SSe- 


e0  = 


Table  XLVI  shows  the  method  of  reducing.  The  curve,  Fig. 
115,  is  drawn  from  the  equation  p  =  0.0117  (e  —  72. 2) 2.  The 
circles  show  the  experimental  values,  and  indicate  where  the 
losses  deviate  from  the  quadratic  law. 


126 


DIELECTRIC  PHENOMENA 


Table  XL VII  gives  a  similar  set  of  data  for  a  small  wire.     The 
results  are  plotted  in  Figs.  117  and  118. 


=  3 


60 


Ji 


50   60    70    80    90  100  110  120  130  140  150  Between  Lines 
25          35          45          55          65  75  To  Neutral 

Kilo-VoTts  Effective 

FIG.  117. — Characteristic  corona  loss  curve  for  small  wire. 
No    8    copper    wire.     Diameter,   0.328  cm.     Total  length,  29,050  cm. 
Spacing,  0.328  cm.     Table  XLVII,  Line  B. 


- 

0 

,(** 

^ 

^ 

P*' 

^ 

^ 

•^ 

0^" 

f> 

** 

^ 

*/' 

\ 

\S* 

^4 

Y'A 

"" 

40           60           80          100         120         140         160         180          200 
20          80           40           50          60          70           80          90          IM^ 

Kilo-Volts  Effective                                          To  Neutr»l 

FIG.  118. — Corona  loss  curve  plotted  between  \/pand  e.-    (Smallconductor. 
Data  same  as  Fig.  117.) 


CORONA  LOSS 


127 


TABLE  XLVII. — CORONA  Loss 
SA    Method  of  Reducing 


Kilovolts  between 
line  e' 

Kilovolts  to 
neutral  e 

Kilowatt  line 
loss  p 

VP 

70.0 

35.0 

0.02 

0.14 

80.0 

40.0 

0.07 

0.26 

91.2 

45.6 

0.26 

0.51 

101.3 

50.6 

0.85 

0.92 

110.0 

55.0 

1.42 

1.19 

120.0 

60.0 

2.02 

1.42 

130.0 

65.0 

2,71 

1.65 

141.5 

70.7 

3.51 

1.87 

70.0 

35.0 

0.06 

0.24 

80.0 

40.0 

0.10 

0.32 

90.5 

45.2 

0.26 

0.51 

101.3 

50.6 

0.96 

0.98 

109.9 

54.9 

1.43 

1.20 

152.0 

76.0 

4.45 

2.11 

160.4 

80.2 

5.17 

2.27 

170.1) 

85.0 

6.06 

2.46 

180.6 

90.3 

7.04 

2.65 

190.6 

95.3 

8.26 

2.87 

200.0 

100.0 

9.52 

3.08 

193.6 

96.8 

8.60 

2.93 

176.0 

88.0 

6.65 

2.58 

155.0 

77.5 

4.66 

2.16 

136.0 

68.0 

3.01 

1.73 

Total  conductor  length 29,050  cm. 

Spacing 183  cm. 

No.  8  H.  D.  copper  wire — diameter 0.328  cm. 

Temperature 1.5 

Barometer  .  .  .76.6 


S  Se        =  841.1  ASe        =  93.7 

S  2\/P  =    24.15         AZ\/p  =    3.80 


100 

.0 

3 

08 

80 

.2 

2 

.27 

96 

.8 

2 

.93 

77 

.5 

2 

.15 

95 

.3 

2 

,87 

68 

.0 

1 

.73 

90 

.3 

2. 

65 

60 

.0 

1 

.42 

85 

.0 

2 

46 

88 

.0 

2 

.58 

467 

.4 

13 

.99 

373 

.7 

10 

.15 

841.1  - 


24.15 
0.0410 


10 
=  =0.0410 


c2  =  0.00168 

p  =  0.00168(e  -25.2)2 


128 


DIELECTRIC  PHENOMENA 


To  further  investigate  the  law  it  is  now  necessary  to  determine 
the  various  factors  affecting  e0  and  c2.     These  will  be  taken  up 


1 

!§ 

l 

( 
( 

x 

X 

^ 

ps 

^ 

Jf 

X 

^c 

^J 

e 

V     j 

*r* 

^ 

•^~ 

)     20     40     60     80    100   120   140   160   180   200  22 
Between  Line 
)     10     20    30     40     50    60     70     80     90    100  1 
Kilo-Volts  Effective         To  Neutn 

FIG.  119. — Corona  loss  plotted  between  Vp  and  e  to  illustrate  the 

quadratic  law. 

Phosphor-bronze  conductor.    Diameter,  0.051  cm.    Spacing,  366  cm.  Total 
length,  29,050  cm.     Temp.,— 6.5°  C.    Bar.,  77.3  cm.     Line  B. 

under  separate  headings.     The  loss  near  the  critical  point  will 
then  be  discussed. 

In  Fig.  119,  \/p  and  e  are  plotted.     This  is  an  especially  inter- 
esting curve  on  account  of  its  range.     The  measurements  are 


s 

* 

x* 

^ 

** 

S 

e( 

) 

/; 

1 

S 

20    40    60    80  100  120  140  160  180  200 
10    20    30  40   60    60   70    a 

Kilo-  Volts  Effective 


To  Neutral 


/ 

/ 

X 

< 

'V 

/ 

j 

X 

e 

0 

/ 

>•-< 

00         120         140         ICO        180        200       22C 
Between  Line 
50          60          70           80          90         100        11 
Kilo-  Volts   Effective      To  Neutra 

FIG.  120.  FIG.  121. 

Corona  loss  plotted  between  \/p  and  e  to  illustrate  the  quadratic  law. 
FIG.  120. — No  8  copper  wire.  Diameter,  0.328  cm.  Total  length,  29,050 

cm.     Spacing,  244  cm.     Temp.  1.5.     Bar.,  76.6.     Line  B. 

FIG.  121. — 3/o,  7-strand  weathered  cable.     Diameter,  1.18  cm.     Spacing, 

310cm.     Total  length,  109,500  cm.     Temp.,  16.     Bar.,  75.3.     Line  A. 

taken  up  to  20  times  the  disruptive  critical  voltage,  and  show 
how  well  the  quadratic  law  holds.  Figs.  120  and  121  are  plotted 
in  the  same  way  to  illustrate  the  quadratic  law. 


CORONA  LOSS 


129 


Frequency. — To  determine  the  way  that  frequency  enters  into 
the  power  equation 

p  =  c*(e  -  e0)* 

a  series  of  loss  curves  were  taken  on  line  A  at  various  frequencies. 

These  tests  indicated  that  the  loss  varied  almost  directly  with 

the  frequency  over  the  range  investigated.     The  data  are  given  in 

Tables  XL VIII  and  XLIX.     Thus  when  the  frequency  does  not 

TABLE  XL VIII.— LINE  A.    CONDUCTOR  2-3.    TOTAL  LENGTH  54,750  CM. 


Kilovolts  between 
lines 

210 

200 

190 

180 

/ 

Kilowatts  loss 

47 

4.9 

3.2 

.  2.0 

1.3 

60 

5.1 

3.7 

2.6 

1.6 

70 

6.1 

4.3 

2.8 

1.7 

80 

6.9 

5.0 

3.4 

1.9 

3  6 

2  1 

90 

7.5 

5.6 

3.8 

2.6 

100 

8.0 

5.6 

3.7 

2.4 

115 

9.3 

7.1 

5.0 

3.4 

TABLE  XLIX. — LINE  A.    CONDUCTORS  1-2-3-4.    TOTAL  LENGTH  109,500  CM. 


Kilovolts  between 
lines 

210 

200 

190 

180 

/ 

Kilowatts  loss 

50 

9.24 

6.30 

3.80 

2.20 

60 

10.50 

7.30 

4.65 

2.65 

70 

12.1 

8.60 

5.50 

3.20 

80 

14.0 

10.20 

6.80 

3.95 

vary  greatly  from  60  cycles  the  equation  may  be  written 

p  =  af(e  -  e0)2 

It  was  then  decided  to  make  the  investigation  over  a  greater 
range  of  frequency,  and  on  shorter  lines  to  prevent  wave  distor- 
tion due  to  load,  etc.  These  measurements  were  made  on  the 
indoor  line.  Table  L  gives  data  for  a  0.333-cm.  radius  wire.  Care 
was  taken  to  keep  the  wave  shape  as  nearly  constant  as  possible. 
The  results  are  plotted  in  Fig.  122.  e0  is  the  same  for  all  fre- 


130 


DIELECTRIC  PHENOMENA 


TABLE  L. — CORONA  Loss  AT  DIFFERENT  FREQUENCIES 


New  Galvanized  Cable 

Radius  =  0.334  cm. 
Spacing  =  61  cm. 
Effective  kv. 


Total  length  =  0.0815  km. 

6  =  1.00 
Indoor  line 


Kilovolts  to 
neutral  en 

Kilowatts  per 
km.  (p) 

V* 

Kilovolts  to 
neutral  en 

Kilowatts  per 
km.  (p) 

va 

Kilovolts  to 
neutral  en 

Kilowatts  per 
km.  (p) 

va 

Kilovolts  to 
neutral  en 

Kilowatts  per 
km.  (p) 

va 

Test  5QB,  40  cycles 

Test  .515,  60  cycles 

Test  52B,  90  cycles 

Test  535,  120  cycles 

50.5 

1.10 

1.05 

54.0 

3.31 

1.82 

89.5 

61.5 

7.84 

45.0 

0.67 

0.82 

53.5 

2.57 

1.59 

62.5 

9.15 

3.02 

85.8 

54.0 

7.35 

50.7 

2.88 

1.69 

56.2 

4.15 

2.04 

68.0 

14.55 

3.88 

87.0 

56.0 

7.48 

53.7 

6.73 

2.59 

59.2 

5.84 

2.42 

72.0 

20.10 

4.48 

82.8 

48.2 

6.93 

56.2 

10.30 

3.21 

64.0 

9.10 

3.02 

78.0 

28.45 

5.20 

77.5 

37.50 

6.13 

60.2 

15.60 

3.94 

66.8 

11.55 

3.40 

87.3 

40.20 

6.32 

74.0 

31.60 

£.64 

69.0 

30.00 

5.46 

71.5 

15.95 

3.99 

91.5 

49.70 

7.02 

66.0 

18.90 

4.35 

72.7 

37.40 

6.10 

ra.7 

18.44 

4.30 

82.0 

34.60 

5.83 

60.4 

12.75 

3.75 

71.0 

32.00 

5.65 

70.7 

15.23 

3.95 

72.8 

21.10 

4.67 

50.3 

4.90 

1.40 

75.5 

41.30 

6.42 

67.5 

12.30 

3.50 

52.7 

5.23 

2.90 

54.3 

5.02 

2.24 

81.0 

53.50 

7.30 

65.0 
60.2 

58.2 
46.7 

10.20 
6.64 

5.28 
0.80 

3.36 

2.58 

2.29 
0.89 

56.0 
61,5 

67.2 
70.2 

5.65 
10.20 

15.75 
19.30 

2.32 
3.20 

3.90 
4.38 

58.4 

9  45 

3.08 

87.5 
95.0 

80.0 
75.5 
70.5 

66.5 
59.5 

69.80 
90.00 

51.20 
41.50 
29.70 

25.60 
13.65 

8.35 
9.50 

7.15 
6.42 
5.42 

5.06 
3.69 

VFpar  Km  of  Cond  M 
_,Ne&.t>.cicn-JCO«oo 

? 

1 

% 

J 

x 

s^, 

' 

X" 

) 

? 

s 

X 

^ 

/ 

y 

s* 

/ 

*4 

*<*< 

& 

^ 

/* 

& 

S 

30 


40       50       60       70       80       90 
Effective  Kilo-Volts  to  Neutral 


100 


FIG.  122. — Corona  loss  curves  at  different  frequencies.     (Plotted  from 

Table  L.) 


quencies  but  the  slope  c  varies  with  the  frequency.  Values  of  c2 
for  various  frequencies  from  30  to  120  cycles  and  three  different 
sizes  of  conductor  are  given  in  Table  LI,  and  plotted  in  Fig.  123. 


CORONA  LOSS 


131 


TABLE   LI. — VARIATION    OF    c2    WITH    FREQUENCY 
(Indoor  Line) 


Tests  1-6B 

Tests  37-40B 

Tests  50-53  B 

r  =  0.032  cm. 

r  =  0.105  cm. 

r  =  0.334  cable 

s  =  61  cm. 

s  =  61  cm. 

Fre- 
quency 

Length  =  0.0815  km. 
5  =  1.00 

Length  =  0.0815 
5  =  1.00 

s  =  61  cm. 
Length  =  0.0815 

c2  per  km. 

e0 

c2  per  km. 

e0 

c2  per  km. 

e0 

30 

0  0052 

9  5 

0  0071 

21  5 

40 

0.0061 

9.5 

0.0092 

21.5 

0.0139 

38.0 

60 

0.0078 

9.5 

0.0119 

20.5 

0.0173 

38.0 

75 

0  0092 

9  5 

0.0144 

20.5 

38.0 

90 

0.0107 

9.5 

0.0157 

20.5 

0.0240 

38.0 

120 

0.0134 

9.5 

0.0203 

19.0 

0.0297 

38.0 

The  points  over  this  measured  range  lie  on  a  straight  line,  and 
this  line  extended  cuts  the  frequency  axis  at  —  25.     This  seems 


.036 
.032 
.028 
.024 

.020 

> 
.016 

.012 
.008 
.004 
0 

s 

?\ 

2- 

£* 

f 

/ 

/ 

r*, 

>  (  s_ 

/ 

^ 

y 

f 

/ 

/ 

o. 

s 

£r- 

/ 

/ 

Y< 

/ 

/ 

^4 

-^ 

/ 

^ 

'S 

^ 

** 

/ 

/ 

^ 

^ 

/ 

^ 

' 

^ 

v^ 

•^x 

^ 

" 

'*> 

0   20   40  60   80  100  120 

Frequency 


.uie  - 

012 

010 

1 

'* 

o 

AftO 

'\° 

°\ 

^s 

N 

004 

V 

0 

^ 

0 



0  - 

1000  2000  3000  4000  5000  6000  7000 


FIG.  123. — Variation  of  c2  with  fre-      FIG.  124. — Variation  of  c2  with  s/r. 
quency.     (Data  from  Table  LI.) 

to  mean  for  a  given  wire  and  spacing  a  constant  loss  plus  a  loss 
which  varies  directly  as  the  frequency. 
The  equation  may  be  written 

At  zero  frequency  the  equation  reduces  to 
p  =  25a(e  -  e0)* 


132 


DIELECTRIC  PHENOMENA 


This  is  not  necessarily  the  direct-current  loss  but  is  probably 
lower  as  the  maximum  voltage  is  applied  for  less  time.  Watson 
has  made  laboratory  measurements  of  d.c.  loss,  using  an  influence 
machine  as  the  source  of  power.1  Some  of  these  measurements 
are  compared  with  the  a.c.  loss  in  Table  LII,  for  the  same  maxi- 
mum voltages;  the  difference  between  the  d.c.  loss  and  the  a.c. 
loss  for  the  same  effective  voltages  is  much  greater. 

TABLE  LII. — COMPARISON  OF  D.C.  CORONA  Loss  WITH  Loss  AT  60   CYCLES 
FOR  SAME  MAXIMUM  VOLTAGE 


Voltage 
gradient 
0 

D.c. 
amps. 
» 

D.c. 

kilovolts 
e 

D.c. 

loss 

p 

kw./km. 

Corresponding 
a.c.  effective 
kilovolts 
e\ 

Measured 
60-cycle  loss 
Pi 
kw./km. 

Ratio 
60  cycles 
d.  c.  loss 
ft 
P 

61 

0.003 

55 

0.16 

39.8 

0.25 

1.52 

66 

0.004 

59 

0.24 

42.0 

0.37 

1.58 

69 

0.005 

62 

0.31 

44.0 

0.50 

1.61 

75 

0.007 

67 

0.47 

48.0 

0.80 

1.67 

s  =  100  cm.  r  =  0.0597  cm. 

D.c.  measurements  from  Watson,  Institute  of  Electrical  Engineers. 

Relation  between  c2  and  s/r. — The  power  equation  may  be 
written  over  the  commercial  range  of  frequency 

p  =  c\e-eoy  =  a(/+25)(e-e0)2 

where  the  relation  between  c2  and  s/r  has  not  to  this  point  been 
investigated.  The  relation  will  first  be  determined  for  the  prac- 
tical sizes  of  conductors  at  practical  spacings  of  the  outdoor  line, 
and  later  over  greater  range  from  the  indoor  data.  Only  60- 
cycle  values  will  be  used,  as  the  data  at  this  frequency  are  very 
complete.  In  Table  LIII  are  values  of  c2  for  various  sizes  of 
wire  and  cable  at  various  spacings.  c2  varies  greatly  with  the 
radius  of  the  conductor  r  and  the  spacing  s.  Plotting  s/r  and 
c2  a  curve  is  obtained  that  suggests  a  hyperbola.  The  curve 
between  log  c2  and  log  s/r  is  a  straight  line.  Therefore  the  follow- 
ing relation  between  c2  and  s/r  is  established. 


c2  =  A  (s/r}d 


(33) 


The  fair  weather  value  of  c2  for  standard  line  A  1-2-3-4  may 
now  be  examined  in  Table  LIV. 

1  Watson,  Journal  Institution  of  Electrical  Engineers,  June,  1910. 


CORONA  LOSS  133 

TABLE  LIII. — EXPERIMENTAL  VALUES — LINES  A  AND  B 
Relation  between  C2  and  s/r 


Test 
No. 

Diameter, 
cm. 

s 

f 

5 

C2    X    10* 

per  km. 

Style  of 
conductor 

Material 

95 

0.168 

6550 

1.07 

280 

Wire 

Gal.  iron 

92 

0.168 

4880 

1.07 

256 

Wire 

Gal.  iron 

86 

0.168 

3700 

1.08 

326 

Wire 

Gal.  iron 

138 

0.328 

2980 

1.10 

331 

Wire 

Copper 

94 

0.168 

2730 

1.07 

410 

Wire 

Gal.  iron 

137 

0.328 

2230 

1.10 

391 

Wire 

Copper 

91 

0.168 

1820 

1.07 

506 

Wire 

Gal.  iron 

128 

0.518 

1530 

1.05 

412 

Wire 

Copper 

136 

0.328 

1490 

1.10 

513 

Wire' 

Copper 

82 

.0.585 

1480 

1.07 

513 

Cable 

Gal.  iron 

135 

0.328 

1120 

1.10 

570 

Wire 

Copper 

94o 

0.168 

1090 

1.07 

633 

Wire 

Gal.  iron 

77 

0.585 

1060 

1.07 

543 

Cable 

Gal.  iron 

79 

0.585 

770 

1.08 

571 

Cable 

Gal.  iron 

134 

0.328 

740 

1.10 

772 

Wire 

Copper 

126 

0.518 

700 

1.11 

687 

Wire 

Copper 

18 

1.181 

525 

1.02 

950 

Cable 

Copper 

80 

0.585 

520 

1.07 

^       784 

Cable 

Gal.  iron 

125 

0.518 

350 

1.11 

1070 

Wire 

Copper 

73 

0.585 

310 

1.07 

1018 

Cable 

Gal.  iron 

100 

0.953 

193 

1.08 

1584 

Cable 

Gal.  iron 

TABLE  LIV. — RELATION  OF  c2  TO  T  FOR  MAIN  EXPERIMENTAL  LINES 

o 

Line  A  1-2-3-4 
(Standard  Line  A) 


Test  No. 

C2    X    105 

per  km. 

1 

•   5 

8 

Test  No. 

C2    X    105 

per  km. 

l 
i 

s 

18 

945 

0.982 

1.020 

103 

980 

0.901 

1.112 

36 

1050 

0.966 

1.037 

104 

892 

0.878 

1.138 

37 

945 

0.959 

1.043 

105 

890 

0.866 

1.158 

84 

945  t 

0.933 

1.074 

109 

869 

0.928 

1.078 

101 

955 

0.925 

1.081 

119 

991 

0.888 

1.127 

It  is  seen  that  these  values  are  not  exactly  constant  but  appar- 
ently vary  with  the  temperature  and  barometric  pressure,  c2 
and  1/5  in  curve,  Fig.  125,  suggest  that  c2  varies  as  1/6.  Multi- 
plying by  5  then,  reduces  c2  to  the  standard  temperature  of  25 

9 


134 


DIELECTRIC  PHENOMENA 


TABLE  LV 

(Corrected  c2  and  s/r) 


Test  No. 

Diam- 
eter, cm. 

s/r 

C2    X    105 

read 
per  km. 

corrected 
to  25°  C., 
76  cm. 

Corr. 
factor  5 

corrected 
to  25°  C., 
76  cm. 

log  — 
r 

Style  of 
conductor 

bar. 

bar. 

95 

0.168 

6550 

280 

300 

1.07 

5.704 

8.787 

Wire 

92 

0.168 

4880 

256 

275 

1.07 

5.620 

8.492 

Wire 

86 

0.168 

3700 

326 

347 

1.08 

5.852 

8.215 

Wire 

138 

0.328 

2980 

331 

364 

1.09 

5.892 

8.000 

Wire 

137 

0.328 

2230 

391 

429 

1.09 

6.062 

7.709 

Wire 

77 

0.585 

1060 

543. 

582 

1.07 

6.372 

6.966 

Cable 

126 

0.518 

7QO 

687 

755 

.10 

6.637 

6.551 

Wire 

18 

1.181 

525 

950 

965 

.02 

6.821 

6.263 

Cable 

80 

0.585 

520 

784 

840 

.07 

6.733 

6.254 

Cable 

125 

0.518 

350 

1070 

1190 

.11 

7.083 

5.858 

Wire 

73 

0.585 

310 

1018 

1090 

.07 

6.995 

5.763 

Cable 

100 

0.953 

193 

1584 

1710 

.08 

7.405 

5.263 

Cable 

.020 
.015 

.005 


.2  .4  .6    ys       .8  1.0 

FIG.  125. — Relation  between  c2  and  1/5. 


1.2 


TABLE  LVI. — SA  REDUCTION  OF  RELATION  OF  c2  TO  - 
(c2  Corrected  to  25  deg.  C. — 76  cm.  Barometric  Pressure) 


Test  No. 

loge  (cnO*) 

8 

loe*  7 

Test    No. 

log*  (cnos) 

3 
loge  — 

95 

5.704 

8.787 

126 

6.637 

6.551 

92 

5.620 

8.492 

18 

6.871 

6.263 

86 

5.852 

8.215 

80 

6.733 

6.254 

138 

5.892 

8.000 

125 

7.083 

5.858 

137 

6.062 

7.709 

73 

6.995 

5.736 

77 

6.372 

6.966 

100 

7.444 

5.263 

35.502 

48.169 

41.763 

35.925 

CORONA  LOSS 


135 


Si  Iog6(c2105)  =    35.50 


loge  -  =  48.17 


S2loge(c2105)  =    41.76  S2  logc     = 


35.92 


d= 


AS  Ioge(c2105)  =  -6.26  AS  loge      =  12.25 

SS  Ioge(c2105)  =  77.26  SS   loge  *  =  84.09 

AS  logec2  X  105        -6.26 
-~ 


AS  loge  - 
log  (C2105)    -  dSS  loge  - 


=9.92 


log  (c2106)  =  -0.5  loge  ~  +  9.92 


c2  =  20,500  -J-10-1 

\  s 


deg.  C.  and  76  cm.  barometric  pressure.  This  particular  correc- 
tion is  not  satisfactory  as  the  range  of  5  is  small.  It  seems  the 
best  until  more  complete  data  are  obtained.  In  Table  LV  all 
values  of  c  are  corrected  to  25  deg.  C.  and  76  cm.  barometer, 
and  the  constants  calculated  by  the  SA  method  in  Table  LVI. 
This  gives:  c2  =  20,500Vr/s  X  10 ~5  per  km.  of  total  conductor 
at  25  deg.  C.,  76  cm.  barometer  and  60  cycles. 

Curve  124  is  plotted  from  the  points  calculated  in  Table  LVII, 
while  the  circles  show  the  actual  experimental  points. 

TABLE  LVII. — CALCULATION  OF  CURVE  No.  124  FROM 
( c2  X  10*  =  20,500 


8 

r 

V:: 

c2  X  106 

s 
r 

£ 

c2  X  10* 

250 

0.0633 

129 

2000 

0.0224 

460 

500 

0.0447 

915 

3000 

0.0183 

376 

1000 

0.0316 

648 

4000 

0.0158 

324 

1500 

0.0258 

530 

6000 

0.0128 

262 

Curve  126  shows  a  straight-line  relation  between  log  s/r  and 
log  c2.  The  equation  for  the  power  loss  at  25  deg.  C.  and  76  cm. 
barometric  pressure  and  any  frequency  may  now  be  written 


p  =  241(/  +  25)\/r/s(e  - 


(34) 


136 


DIELECTRIC  PHENOMENA 


where  p  =  the  energy  loss  per  kilometer  of  conductor  in  kilo- 
watts. 

e    =  kilovolts  to  neutral. 

e0  =  disruptive  critical  kilovolts  to  neutral  at  25  deg.  C. 
and  76  cm.  barometric  pressure. 

/    =  the  frequency  in  cycles  per  second. 

r   =  the  radius  of  .the  conductor  in  cm. 

s   =  the  distance  between  conductor  centers  in  cm. 

The  value  of  e0  varies  with  the  radius  of  the  conductor  r,  and 
the  spacing  s,  and  will  be  discussed  later. 

Relation  between  c2,  and  r  and  s  for  Small  Conductors  and 
Small  Spacings.  (Indoor  Line). — The  loss  was  investigated 
for  very  small  conductors  at  large  and  small  spacings,  and  for 
large  conductors  at  small  spacings,  on  the  indoor  line.  The 
conductors  ranged  from  0.025  cm.  to  0.46  cm.  in  radius,  and  the 


* 


0123456789 
Loge  -f 

FIG.   126. — Determination  of  equation  between  c2  and  s/r. 


spacings  from  12.5  to  275  cm.  This  investigation  is,  hence,  an 
extension  of  the  above  investigation  beyond  the  practical  range. 
The  quadratic  law  still  holds — the  relation  between  c2,  r  and  s, 
however,  becomes  more  complicated.  This  is  also  true  of  the 
disruptive  critical  voltage.  Below  a  spacing  of  about  15  cm. 
it  is  difficult  to  express  the  loss  in  terms  of  a  law,  as  the  results 
are  erratic,  probably  due  to  the  great  distortion  of  the  field  which 
is  augmented  when  the  corona  starts,  greatly  increasing  the  loss 
above  the  quadratic. 

For  conductors  0.025  cm.  in  radius  and  above,  and  15  cm. 
spacing  and  above,  this  data  shows  that 


r  +  -  +  0.04 


c2  =  20,500, 


10~5  per  km.  of  conductor      (33d) 


CORONA  LOSS 


137 


The  more  complete  equation  is,  therefore, 


p  =  241  (/  +  25). 


r  +  -  +  0.04 


(e  -  edY  10-5  kw./km. 
of  conductor1 


50 


In  Fig.  127  the  points  are  measured  corona  loss  values,  while  the 
curve  is  calculated  from  equation  (34a)  (r  =  0.032,  spacings  46 
and  275  cm.).  Data  are  given  in  the  appendix. 

It  is  interesting  to  note  from  (33a)  that  as  r  becomes  very 
small  the  c2  term,  at  a  given 
spacing,  approaches  a  con- 
stant value — somewhat  as  if 
the  corona  diameter  acts  as 
the  conductor  diameter. 

The  Disruptive  Critical 
Voltage.  —  The  point  of 
greatest  stress  around  a  cylin- 
drical conductor  is  at  its  sur- 
face. When  s/r  is  large  the 
gradient  at  the  surface  of  the 
conductor  may  be  expressed 

de  e 


40 


M20 


10 


rf£^ 


20 


40         60          80        100 
6  -  K.V.  to  Neutral 


120 


r  loge  s/r 


(12c) 


to 


FIG.  127. — Comparison  of  calculat- 
ed and  measured  corona  loss  for  small 
conductors  at  small  and  large  spacings. 

(Points  measured.  Curves  calculated 
from  equation  (34o)  Conductor  radius, 
0.032  cm.  Spacings,  46  cm.  and  275 
cm.  5  =  1.01.) 


where   e  =  the    voltage 

neutral. 

s  =  distance  between  conductor  centers. 
r  =  the  radius. 

When  r  and  s  are  in  centimeters  and  e  is  in  kilovolts,  g  is  ex- 
pressed in  kilovolts  per  centimeter.  If  e0,  which  has  been  called 
the  disruptive  critical  voltage,  is  taken  for  e, 

e0 

=  r  loge  s/r 

g0  then  is  the  stress  at  the  conductor  surface  corresponding  to  e0, 
and  will  be  called  the  disruptive  gradient,  to  distinguish  it  from  the 
visual  gradient  gv.  Values  of  g0  for  wires  and  cables  taken  under 
a  variety  of  conditions  on  the  outdoor  line  are  given  in  Tables 
LVIII  and  LIX.  These  values  are  corrected  to  standard  tem- 
perature and  pressure  by  dividing  by  8. 

1  F.  W.  Peek,  Jr.,  High  Voltage  Engineering,  Journal  Franklin  Institute, 
Dec.,  1913. 


138 


DIELECTRIC  PHENOMENA 


TABLE  LVIII. — DISRUPTIVE  CRITICAL  VOLTAGE  GRADIENT  FOR  WIRES 
(Values  Corrected  to  76  cm.  Barometer  and  25  deg.  C.,  Outdoor  Line) 


Test  No. 

Spacing,  cm. 

Radius,  cm. 

g.  kv./cm. 
max. 

Per  cent, 
variation 
from  mean 

Per  cent, 
variation 
max.  to  min. 

91 

152.0 

0.084 

31.3 

94 

229.0 

31.6 

92 

410.0 

29  1 

95 

550.0 

36.5 

134 

122.0 

0  164 

Avg.  =30.9 
28.8 

5.8 

7.9 

135 

183.0 

27  1 

136 

244.0 

29.0 

137 

366.0 

25.7 

138 

488.0 

25  3 

125 

91  4 

0  259 

Avg.  =27.2 

28  7 

7.0 

12.7 

126 

183  0 

26  5 

127 

275.0 

26.0 

128 

397.0 

26  2 

122 

91  4 

0  463 

Avg.  =26.9 

28  7 

6.7 

9.4 

123 

183  0 

30  4 

120 

214  0 

30  5 

124 

275  0 

31  0 

Avg.  =30.1 

4.8 

7.6 

Total  Avg.  29.0 

If  the  values  of  e0  for  standard  line  A  (1.8  cm.  seven-strand 
cable)  are  examined  it  is  found  that  the  average  value  of  g0  is  25.8 
kv.  per  centimeter  maximum.  For  cables  between  0.583  cm.  and 
1.18  cm.  in  diameter  and  various  spacings,  the  average  value  of  g0 
is  25.6  kv.  per  centimeter  maximum,  or,  in  other  words,  g0  is 
constant  for  commercial  sizes  of  cables,  at  practical  spacings,  and 
is  25.6  kv.  per  centimeter  maximum.  In  determining  the  value 
g0  for  seven-strand  cables  r  was  taken  for  convenience  as  the 
outside  radius.  Hence  the  above  g0  is  not  the  actual  g0  as  ob- 
tained for  wires,  but  is  an  apparent  g0.  The  actual  g0  may  be 


CORONA  LOSS 


139 


obtained  by  taking  some  mean  radius  r2  between  the  outside 
radius  r  and  the  radius  to  the  point  of  contact  of  the  outside 
strands  r\.  r2  approaches  r  in  value  as  the  number  of  strands  is 
increased. 

TABLE  LIX. — DISRUPTIVE  CRITICAL  VOLTAGE  GRADIENT  FOR  CABLES 
(Values  Corrected  to  76  cm.  Bar.  and  25  deg.  C.,  Outdoor  Line) 


Test  No. 

Spacing,  cm. 

Radius,  cm. 

g.  kv./cm. 
max. 

Per  cent, 
variation 
from  mean 

Per  cent, 
variation 
max.  to  min. 

73 

91.4 

0.292 

26.5 

80 

152  0 

24  0 

79 

244.0 

23.9 

77 

310.0 

23  9 

'       82 

432.0 

25.0 

100 

91.4 

0.476 

Avg.  =  24  .  7 
25  5 

7.3 

9.8 

115 

91.4 

26.2 

116 

183.0 

26.0 

117 

275.0 

26.4 

118 

366.0 

28.1 

18 

310.0 

Line  A 
0.590 

Avg.  =26.4 
-  1.  2.  3.  4 
25.5 

6.4 

9.3 

36 

310.0 

26.0 

37 

310.0 

25  3 

84 

310.0 

25.8 

101 

310.0 

26.5 

103 

310.0 

26  1 

104 

310.0 

25  7 

105 

310.0 

26.0 

109 

310.0 

25  8 

119 

310.0 

25.1 

119 

310.0 

26.0 

, 

Total 

Avg.  =25.8 
Avg.  =  25  .  7 

2.7 
5.5 

5.3 
8.1 

The  values  of  g0  for  wires  varying  in  diameter  from  0.168  cm. 
to  0.928  cm.  and  for  spacings  from  90  to  600  cm.  are  constant 
within  the  limits  of  experimental  error.     This  more  than  covers 
the  commercial  range.     The  mean  max.  value  is: 
g0  =  29  kv.  per  cm.  at  25  deg.  C.,  and  76  cm.  barometric  pressure. 


140 


DIELECTRIC  PHENOMENA 


Considerable  variation  should  'be  expected  in  g0  values  obtained 
on  a  long  outdoor  line,  due  to 

1.  Necessarily  imperfect  conductors,  kinks,  etc.,  in  an  outdoor 
line  of  this  length. 

2.  Progressive  change  in  the  value  of  successive  points  on  a 
given  curve  due  to  slight  changes  of  wave  shape,  etc.,  as  the  vol- 
tages are  increased,  and  the  apparent  shift  of  e0. 

The  close  agreement  of  g0  for  wires  is  for  the  above  reasons 
remarkable. 

Discrepancies  due  to  progressive  change  are  not  to  be  expected 
for  standard  line  A  to  any  great  extent  as  the  conductor  spacing 
was  always  the  same,  and  test  conditions  were  kept  as  nearly 
constant  as  possible. 


Gradient  Max,  K.V,  per  en 

o  S  8  8  fe  § 

0* 

29.8 
\ 

Avsi 

x 

X 

n 

^ 

g~ 

25.7 

Avsr, 

x  = 

0  = 

Wir 
Oab 

3S 

les 

1234567 

Radius  m   cms 

FIG.  128. — 0 . 90  for  wires  and  cables.     (Data  from  Tables  LVIII  and  LIX.) 

The  above  data  shows  that  g0  may  be  considered  constant  for 
diameters  of  conductors  and  spacings  within  the  practical  range. 
This  immediately  suggests  that  g0  is  the  actual  rupturing  gra- 
dient of  air  or  identical  with  g0  of  the  expression  for  visual  corona. 
This  was  further  investigated  over  a  greater  range  on  the  indoor 
line. 

Q0  cables 

-  =  m0 
g0  wires 

where  m0  is  a  fraction  which  approaches  unity  as  the  irregularity 
of  the  surface  is  reduced,  or  number  of  strands  increased. 
Then 

e0  =  8m0g0r  loge  s/r  (35) 

(See  curve,  Fig.  128.) 
The  loss  equation  may  now  be  written 


P  = 


241 


-  e0)*  10~5  kw./km.          (34) 


CORONA  LOSS 


141 


where  p  expresses  the  loss  above  the  visual  critical  voltage  ev,  and 
e0  is  given  in  (35). 

Investigations  on  the  indoor  line  over  a  range  covering  small 
conductors  show  that  the  disruptive  gradient  may  be  considered 
for  all  practical  purposes,  constant  when  the  conductor  radius  is 
greater  than  0.20  cm.  As  the  size  of  the  conductor  is  decreased 
the  disruptive  gradient  increases  very  rapidly.  If  the  disruptive 
gradient  for  any  size  of  conductor  is  called  g<i  we  have  found  that 
this  law  may  be  expressed: 

0.30  1         \ 

1  +  -7=     /«    .   —    .x  )  (36) 


\/Sr     (1  +  230  r2) 


r  log,  - 


(35a) 


150 
140 
130 
120 
110 

a  100 


20 


0    .1    .2    .3    .4   .5    .6    .7    .8    .9    1.0 

Radius  iu  cm. 

FIG.  129. — Comparison  of  gv,  gd,  and  g0.     (gd  values  from  Table  LX.) 


Thus,  when  r  is  large  (above  0.2  cm.)  practically  gd  =  g0,  and 
where  r  =  o,  gd  =  gv. 

This  apparent  increase  in  disruptive  gradient  for  small  con- 
ductors gives  the  impression  that  the  residual  from  the  very  highly 
ionized  air«resulting  at  each  cycle  in  effect  increases  the  size  of  the 
conductor.  Thus,  the  gd  formula  is  the  same  as  the  gv  formula 
with  the  energy  distance  term  apparently  modified  or  lessened  by 
the  residual  ionization  at  each  cycle.  g0  results  for  large  conduct- 
ors. Measured  values  of  gd  for  different  conductors  on  the  indoor 
line  are  given  in  Table  LX.  Calculated  and  measured  values  are 
plotted  in  Fig.  129. 

The  corona  loss  equation  over  a  greater  range  of  conductor 
diameter  and  spacing  may  thus  be  written 


142 


DIELECTRIC  PHENOMENA 


p  =  241(/+25) 


+  -  +  0.04 


(e  -  ed)210-5kw./km.  (34a) 


where  e<i  is  obtained  from  equation  (35a). 

TABLE  LX 


Test  No. 

r  cm. 

gd  maximum 
measured 

Od  maximum 
calculated 

12  B 

0.032 

67.5 

70.7 

13  B 

0.032 

70.3 

70.7 

14  B 

0.032 

71.0 

70.7 

18  B 

0.032 

71.0 

70.7 

15  B 

0.032 

71.0 

70.7 

16  B 

0.032 

71.0 

70.7 

19  B 

0.032 

69.6 

70.7 

17  B 

0.032 

71.2 

70.7 

20  B 

0.032 

69.5 

70.7 

21  B 

0.032 

69.3 

70.7 

Avg.  =70.0 

27  B 

0.057 

51.7 

51.3 

26  B 

0.057 

51.3 

51.3 

25  B 

0.057 

51.7 

51.3 

24  B 

0.057 

51.3 

51.3 

Avg.  =51.5 

SOB 

0.071 

45.4 

45.4 

33  B 

0.0914 

39.4 

39.4 

32  B 

0.0914 

39.4 

39.4 

42  B 

0.105 

42.2 

37.6 

41  B 

0.105 

42.2 

37.6 

37  B 

0.105 

42.5 

37.6 

Avg.  =42.3 

45  B 

0.164 

36.5 

33.0 

44  B 

0.164 

33.6 

33.0 

Avg.  =35.1 

49  B 

0.256 

30.8 

31.1 

48  B 

0.256 

32.1 

31.1 

47  B 

0.256 

33.2 

31.1 

Avg.  =32.0 

56  B 

0.464 

31.8 

30.2 

55  B 

0.464 

31.8 

30.2 

54  B 

0.464 

31.5 

30.2 

Avg.  =31.7 

CORONA  LOSS 


143 


It  may  be  interesting   to   note  that   equation  (34)   may  be 
written  in  terms  of  the  gradient,  thus 

p  -  A  V^A  (/  +  25)   (log  *)  2  (r2)  (g  -  g0Y  X  10~5 


Fig.  130  shows  measured  curves  plotted  between  g  and  p  for  a 
given  wire  at  three  different  spacings.  These  curves  all  intersect 
the  axis  at  g0  max.  =  30,  at  d  =  1.0. 


4.0 
3.5 
3.0 

I2'5 
^2.0 

a  1.5 
la-  1.0 

.5 

^ 
^ 

? 

;?—  • 

3 

^c 

^ 

^ 

yA 

<3 

^> 

W 

^ 

* 

J 

<^ 

^ 

^ 

§ 

^ 

^1 

'^^ 

Test  Nos. 
...    94 
xxx     94  A. 
o  o  »     95 
Diam.=  .188  cm 

k^ 

^1 

6*_ 

^^^ 

,+** 

' 

0  10 


20  30  40  50  60  70  80  90  100  110  120  130  140  150  160  170  180 

Apparent  Surface  Gradient 


FIG.  130.  —  Relation  between  power  loss  and  apparent  surface  gradient. 

Losses  Near  the  Disruptive  Critical  Voltage  —  e0.  —  If  the  con- 
ductors could  be  made  perfect  no  appreciable  loss  would  occur 
below  the  visual  critical  voltage.  However,  near  the  starting 
point  of  corona  two  effects  occur,-  which  cause  a  deviation  of 
the  loss  from  the  quadratic  law,  equation  (34),  and  which  affect 
the  loss  in  opposite  directions: 

(a)  With  perfect  conductors  loss  of  power  does  not  begin  at 
the  voltage  ea,  at  which  the  disruptive  gradient  is  reached  at  the 
conductor  surface,  but  only  after  the  disruptive  strength  of  air 
has  been  exceeded  over  a  finite  and  appreciable  distance  a  from 
the  conductor,  that  is,  at  a  higher  voltage  ev.  Since  the  con- 
vergency  of  the  lines  of  dielectric  force  is  great  at  the  surface  of 
small  conductors,  with  such  conductors,  a  considerable  increase 
of  the  voltage  is  required  to  extend  the  disruptive  gradient  to 
some  distance  from  the  conductor,  and  ev  is  considerably  higher 
than  e0.  With  such  conductors  there  would  be  no  loss  until  ev 
were  reached.  The  loss  would  then  suddenly  take  nearly  the 
definite  value  calculated  for  this  applied  voltage  from  equation 
(34).  Even  with  polished  conductors,  in  practice  .the  decrease. 
of  loss  below  that  given  by  equation  34  is  appreciable  with  small 
conductors  within  the  range  between  e0  and  evt  as  seen  in  Fig.  131. 


144 


DIELECTRIC  PHENOMENA 


With  large  conductors,   however,   the  less  convergency  of  the 

lines  of  dielectric  force  at  the 
conductor  surface  requires  a 
less  voltage  increase  beyond 
e0  to  extend  the  disruptive 
gradient  to  some  distance 
from  the  conductor;  e0  and  ev 
are  therefore  closer  together, 
and  this  decrease  of  the  loss 
below  the  theoretical  value 
given  by  equation  (34)  is  not 
appreciable. 

(6)  As  the  conductor  sur- 
face can  never  be  perfect, 
some  loss  of  power  occurs  at 
and  below  the  disruptive  criti- 
cal voltage  at  isolated  points 
of  the  conductor,  where  irreg- 
ularities of  the  surface, 
scratches,  spots  of  mud  or 
dirt,  etc.,  give  a  higher  poten- 
tial gradient  than  that  corre- 
sponding to  the  curvature  of 
With  small  conductors,  this  loss  is  rarely 


2.2 
2.0 
1.8 
1.6 
1.4 

ft,  1.2 

II 

1  1'° 

a  -8 

.6 
.4 
.2 

G 
*t 

/ 

/ 

/ 

/I 

i 

1 

1 

\ 

ii 

A 

,L»° 

isured 

Loss 

/ 

^ 

Quad 
.0022 

rutic 

(e- 

•'.)' 

/ 

i 

t, 

y. 

^' 

0               60               80              100            12 
Between  Line 
0               30               40               50              6 
Kilovolts  Effective      To  Neu^al 

FIG.   131. — Corona  loss  for  small  con- 
ductors near  the  critical  voltage. 
No.   8  copper.     Diameter,  .328cm. 
Length,  29,050  cm.     Spacing,  122  cm. 
Temp.  1.5.     Bar.,  76.6.     Line  B. 


1.6 


1.4 


1.2 


1.0 


!   -8 


the  conductor  surface, 
appreciable,  since  the 
curvature  of  the  con- 
ductor surface  is  of 
the  same  magnitude 
as  that  of  its  irregu- 
larities. It  becomes 
appreciable,  however, 
for  larger  conductors, 
as  seen  in  Fig.  132. 
This  excess  of  the  loss 
beyond  that  given  by 
the  quadratic  law 
equation  essentially 
depends  on  the  con- 
ductor surface  and  is  FIG.  132. — Corona  loss^or  large  conductors  near 


a 

ett 

h 

—Me 

asure< 

Loss 

/ 

-Quac 

ratic 

2?  • 

e0y 

)115 

/- 

£ 

,Exc( 

ss  Lo 

8  P  •• 

(e-< 

1 

-—• 

„-•"'" 

e\s 

/ 

\ 

\ 

100  110  120  130  140  150  160  170  ISO  190  200 

Between  Lines 

50  60  70  80  90  1-00 

Kilovolts  Effective  To  Neutral 


the  larger  the  rougher 
or  dirtier  the  surface  is. 


the  critical  voltage.  (Data  same  as  Fig.  115.) 
It  is  a  maximum  at  the  disruptive  critical 


CORONA  LOSS 


145 


voltage  eoj  and  decreases  above  and  below  ev,  and  is  with  fair 
accuracy  represented  by  the  probability  curve: 

-*(«*-•)' 


p  =  qe 


(37) 


where  q  is  a  coefficient  depending  on  the  number  of  spots,  and  h 
is  a  coefficient  depending  upon  the  size  of  spots. 

Snow,  sleet  and  rain  losses  seem  to  be  of  the  same  nature,  but 
frequently  of  far  greater  magnitude. 

Equation  (37)  is  probably  of  no  practical  importance  as  the 
loss  is  small,  and  q  and  h  naturally  cover  a  wide  range  of  values, 
depending  upon  the  condition  of  the  conductor  surface.  Experi- 
mental values  near  e0  are  taken  from  Table  XLIV  and  tabulated 
in  Table  LXI,  together  with  values  calculated  by  the  quadratic 
law.  Corresponding  experimental  and  calculated  values  are 
subtracted  and  also  tabulated. 

TABLE  LXI.— LINE  A  1-2-3-4  PROM  TABLE  XLIV,  TEST  36 
c2  =  0.0117  e0  =  72.2 


Kilovolts  between 
conductors  e' 

Kw.  exp. 

Po 

Kw.  p  = 
0.01  17  (e  -  e0)  2 

Excess  loss 

Pi  =  (Po  —  P) 

log*  Pi 

(e0  v  «)2 

120.4 

0  11 

N 

0  11 

2  40 

146  5 

130.2 

0.15 

0.15 

2.71 

49.0 

139.2 

0.22 

0  22 

3.09 

6  2 

150.0 

0.40 

0.10 

0.30 

3.40 

8.5 

159.0 

0.79 

0.63 

0.16 

2.77 

54.7 

165.8 

1.42 

1.34 

0.08 

2.10 

11.7 

Fig.  132  is  plotted  to  a  large  scale  to  show  the  excess  loss  near 
e0.  As  this  is  for  large  conductors,  e0  and  ev  are  near  together, 
and  the  effect  of  (6)  predominates.  In  order  to  see  if  equation 
(37)  holds,  write 

loge  pi  =  log  q  -  h(e0-  e)2 

Then  the  curve  between  log  pt  and  (e0  —  e)2  should  be  a  straight 
line.     This  is  shown  in  Fig.  133. 

Values  of  q  and  h  are  of  the  following  order  for  Line  A : 


Test  No. 

q  per  cm.  total  conductor 

h 

30 

3.19  X  10-« 

0.0220 

105 

2.47  X  10~6 

0.0208 

103 

2.74  X  10-« 

0.0304 

146 


DIELECTRIC  PHENOMENA 


Fig.  131  is  plotted  from  values  for  a  small  smooth  conductor. 
Here  e0  and  ev  are  far  apart,  and  as  the  curvature  of  the  conductor 
surface  is  of  the  same  magnitude  as  its  irregularities  they  do  not 

greatly  influence  the  loss. 
The  (a)  effect  here  predomi- 
nates— that  is,  the  loss  near  ec 
is  lower  than  that  shown  by 
the  quadratic  law.1 

The  loss  between  e0  and  ev 
is  unstable  as  it  depends  upon 
surface  conditions.  In  all 
cases  the  quadratic  law  is 
closely  followed  above  ev,  and 
on  large  practical  sizes  of  con- 


25 


50 


75 


100        125      150 


FIG.  133. — Determination  of  equa- 
tion (37). 


ductors  with  sufficient  accuracy  over  the  whole  range. 

Temperature  and  Barometric  Pressure. — Values  of  the  dis- 
ruptive critical  voltage  e0  covering  a  considerable  temperature 
range  are  tabulated  in  Table  LXII.  Correction  is  made  to  a 

TJ£BLE  LXII. — TEMPERATURE  AND  DISRUPTIVE  CRITICAL  VOLTAGE  e0 
(Standard  Line  A  1-2-3-4) 


Test 
No. 

Temperature 

Bar.  cm. 

e'0  kv.     - 
bet.  lines 

e'0  corr. 
to  76  cm. 

l/e'0 

Weather 

Wet 

Dry 

18 

16.0 

18.5 

75.5 

138.5 

140.0 

0.00715 

Bright  sun 

15 

20.0 

22.0 

75.2 

140.0 

142.0 

0.00705 

Cloudy  sun 

37 

10.0 

13.0 

75.7 

141  .X) 

142.0 

0.00705 

Bright  sun 

36 

10.0 

12.0 

75.0 

144.2 

146.5 

0.00683 

Cloudy 

109 

-3.0 

-2.0 

73.9 

148.8 

150.8 

0.00663 

Hazy  sun 

84 

1.0 

3.0 

75.2 

149.0 

151.0 

0.00662 

Cloudy 

101 

-1.0 

-1.0 

'  74.7 

153.8 

156.8 

0.00638 

Cloudy 

103 

-4.9 

-4.5 

75.7 

155.3 

156.7 

0.00638 

Sun 

104 

-9.5 

-9.5 

76.2 

157.0 

157.0 

0.00637 

Sun 

119 

-6.5 

-6.0 

76.5 

156.6 

156.1 

0.00642 

Sun 

105 

-13.0 

-13.0 

76.2 

161.0 

161.0 

0.00622 

Sun 

barometric  pressure  of  76  cm.  on  the  assumption  that  e'0  varies 
directly  with  the  pressure.  In  Fig.  134  l/e'0  is  plotted  with 
temperature.  The  straight  line  through  these  points  cuts  the 
temperature  axis  at  —273  deg.  C.  or  absolute  zero.  Temperature 
was  always  measured  in  the  shade.  The  points  that  do  not  fall 
1  This  condition  is  likely  to  obtain  to  a  greater  extent  at  high  altitudes 
as  e0  and  ev  are  farther  apart. 


CORONA  LOSS 


147 


well  on  the  curve  are  the  summer  sunny  day  points.  This  is 
what  would  be  expected,  as  the  conductors  were  at  a  higher  tem- 
perature than  the  temperature  read. 

Fig.  134  shows  that  the  disruptive  critical  voltage  or  the  dis- 
ruptive gradient  varies  inversely  as  the  air  density.  The  data 
range,  however,  is  not  great. 

The  density  of  air  at  25 
deg.  C.  and  76  cm.  barometric 
pressure  is  taken  as  the 
standard. 

Humidity,  Smoke,  Wind. 
Humidity. — Line  A  was  kept 
as  a  standard  throughout  the 
tests.  A  careful  study  of  the 
disruptive  critical  voltage  and 
c2  shows  no  appreciable  effect 
of  either  humidity  or  "  vapor 
products."1  (See  Table 
LXIII.)  Visual  tests,  made 

on  two  short  parallel  wires  indoors  over  a  great  humidity  range, 
also  bear  this  out. 

TABLE  LXIII. — STANDARD  LINE  A.2     CONDUCTORS  1-2-3-4 


_J  °  240  200  160  120  80  40  _  0 
Degrees  C. 


40    60 


FIG.  134. — Effect  of  temperature  on 
e0.     (Data  from  Table  LXII.) 


Test  No. 

Temperature 

Relative 
humidity 

Vapor 
product 

g0  reduced  to 
25  deg.  C.,  76 
cm.  bar. 

Wet 

Dry 

15 

20.0 

22.0 

0.84 

0.55 

18.8 

18 

16.0 

18.5 

0.75 

0.35 

18.5 

36 

10.0 

12.0 

0.78 

0.25 

18.8 

37 

10.0 

13.0 

0.67 

0.21 

18.3 

84 

1.0 

3.0 

0.69 

0.11 

18.7 

101 

-1.0 

-1.0 

1.00 

0.17 

19.2 

103 

-4.9 

-4.9 

1.00 

0.13 

18.9 

104 

-9.5 

-9.5 

1.00 

0.08 

18.6 

105 

-13.0 

-13.0 

1.00 

0.06 

18.8 

109 

-2.0 

-2.0 

1.00 

0.12 

18.7 

Theoretically  there  should  be  no  appreciable  effect  of  humidity 

1  Mershon,  High  Voltage  Measurements  at  Niagara,   A.I.E.E.,  June  30, 
1908. 

2  Line  A  was  kept  at  constant  test  conditions  for  use  as  a  standard  in 
the  study  of  varying  atmospheric  conditions,  etc. 


148  DIELECTRIC  PHENOMENA 

on  e0,  since  even  if  the  water  vapor,  which  may  be  considered  as 
a  gas  dissolved  in  air,  has  a  different  disruptive  gradient  than 
air,  the  percentage  of  the  gas  in  the  .mixture  should  be  too  small 
to  cause  any  appreciable  change.  It  has  been  suggested  that 
" vapor  products"  is  a  measure  of  ionization  and,  in  that  way, 
the  critical  voltage  varies  with  vapor  products.  This  does  not 
seem  likely,  because  with  all  ordinary  atmospheric  air  the  per- 
centage of  ionization  is  so  small  that  it  would  not  be  expected  to 
produce  any  effect.  To  test  this,  the  visual  critical  point  was 
determined  on  two  parallel  wires.  The  room  was  then  closed 
and  the  wires  were  run  at  a  point  very  much  above  this  critical 
point  for  about  an  hour,  or  until  a  very  intense  odor  of  ozone 
filled  the  room.  The  voltage  was  then  removed  and  the  surface 
of  the  wires  cleaned  in  order  to  remove  oxidization.  The  critical 
point  was  then  redetermined  and  found  to  be  the  same,  although 
the  amount  of  ionized  air  was  many  times  that  which  could  be 
expected  in  free  atmospheric  air.  Of  course  if  the  percentage  of 
ionization  were  great  enough,  as  for  instance  in  an  ozone  machine, 
a  change  in  the  disruptive  strength  would  then  be  expected. 

It  has  been  claimed  that  ultraviolet  light  reduces  the  sparking 
point.  This  is  not  borne  out  in  tests,  where  any  quantity  of 
continuously  applied  power  is  involved.  Though  ultraviolet 
light,  ionized  air,  and  various  radiations  cause  the  small  energy 
in  condensers  to  discharge  when  applied  over  comparatively 
great  time ;  in  case  of  large  energy  discharge  in  a  very  short  time, 
as  spark  discharge,  and  corona  due  to  continuously  applied 
voltages,  no  appreciable  effect  should  be  expected,  or  can  be 
observed,  since  the  discharge  which  takes  place  by  ionized  air 
is  not  of  the  same  order  of  magnitude  as  that  produced  by  the 
spark  discharge.  The  time  required  for  a  given  voltage  to  pro- 
duce ionic  saturation  or  discharge,  should,  however,  be  less  with 
high  initial  ionization  than  with  low  initial  ionization.  Hence 
for  impulse  voltages  of  steep  wave  front  and  short  duration,  the 
spark  voltage  may  be  affected  by  initial  ionization.  This  is 
further  discussed  in  Chapters  IV  and  VIII  (page  198). 

It  is  quite  probable  that  humidity  has  some  slight  effect  on 
the  loss  after  corona  has  once  formed  due  to  the  change  of  the 
gas  into  vapor  and  the  agglomeration  of  the  water  particles  by 
the  ions.  This  is  noticed  in  the  spark-over  between  needle  points 
at  very  high  voltage.  In  this  case  there  is  a  very  heavy  brush 
discharge  before  spark-over.  The  sparking  voltage  increases 


CORONA  LOSS  149 

with  increasing  humidity,  due  to  the  fog  formed,  when  there  is 
not  a  mixture  of  two  gases,  air  and  water  vapor,  as  in  the  case 
where  humidity  is  concerned,  but  actual  water  particles  are  in  the 
air.  Steinmetz  has  observed  that  fog  actually  raises  the  striking 
distance  between  needle  points.  The  effect  of  humidity  on  the 
spark  discharge  observed  by  the  author  is  discussed  in  Chapter 
IV.  Greater  loss  should  be  expected  in  corona  measurements 
during  fog  due  to  charge  and  discharge  of  the  water  particles. 
This  causes  loss  at  lower  voltages  and  has  the  effect  of  decreasing 
the  critical  point. 

While  humidity  has  no  effect  on  the  starting  point  of  corona, 
an  effect  might  be  expected  on  the  loss  after  the  discharge  had 
already  started.  The  reason  that  this  is  inappreciable  is  because 
the  corona  discharge  from  wires  covers  very  little  space. 

Smoke. — It  was  difficult  to  get  measurements  to  show  the 
effect  of  smoke,  as  the  prevailing  winds  were  over  the  fields  toward 
the  city.  At  one  time,  however,  during  a  change  in  the  wind 
thick  smoke  was  blown  over  the  line  from  smoke  stacks  of  a  fac- 
tory, and  the  loss  was  increased.  This,  however,  will  probably 
not  be  a  serious  consideration  in  practice. 

Wind. — Losses  measured  during  very  heavy  winds  show  no 
variation  from  losses  measured  during  calm  weather.  That  the 
losses  do  increase  with  increasing  air  velocity  has  been  shown  in 
laboratory  apparatus.  There  is,  however,  no  appreciable  effect 
due  to  the  comparatively  low  air  velocity  in  practice. 

Moisture,  Frost,  Fog,  Sleet,  Rain  and  Snow. — During  some 
of  the  first  tests  it  was  noted  that  the  losses  were  sometimes 
greater  on  the  "going-up  curve"  than  on  the  " coming-down  , 
curve,"  especially  in  the  early  mornings  after  heavy  dew.  The 
losses  became  less  after  the  line  had  been  operated  for  a  while  at 
high  voltage.  Fig.  135  shows  this  well  for  a  conductor  with  a 
coating  of  frost.  This  excess  loss  was  thought  at  first  to  be  due 
to  leakage  through  moisture  on  the  insulators.  Insulators  were 
put  up  without  line  wires,  but  measurements  showed  a  very 
small  insulation  loss  even  during  storms.  It  was  then  concluded 
to  be  due  to  moisture  on  the  conductors  themselves.  Visual  tests  * 
made  on  short  lengths  of  wet  and  dry  cables  showed  this  in  a  very 
striking  manner.  Two  parallel  dry  cables  were  brought  up  to  the 
critical  point.  Water  was  then  thrown  on  the  cables.  What 
had  been  a  glow  on  the  surface  of  the  dry  cables  now  became, 

at  the  wet  spots,  a  discharge  extending  as  much  as  5  to  8  cm. 
10 


150 


DIELECTRIC  PHENOMENA 


from  the  cable  surface. 


5 
4 

-fc 

2 

1 

/ 

/ 

/ 

/ 

e 

0 

j 

V 

/ 

1 

}/ 

C°* 

*~- 

^ 

&<** 

> 

f 

=fp 

r°^ 

*•/ 

z 

This  discharge  reminded  one  of  an  il- 
luminated atomizer. 
Illustrations,  Figs.  67 
and  68  show  this,  but  a 
greater  part  of  the  effect 
is  lost  in  reproduction. 
The  wires  became  quite 
dry  and  down  to  normal 
discharge  after  running 
at  high  voltage  for  a 


50     eo     TO     so      90     ioo    no    120  TO  Neutral  very  few  minutes. 

The  curves,  Fig.  136, 


Kilo.Volts  Effective 


FIG.  135. — Corona  loss  with  frosty  and  dry 
conductors. 


(Conductor  length,  109,500  cm.  Spacing, 
310  cm.  Diameter,  1 . 18  cm.  3/0,7-strand 
cable.  Line  A.  Temp., -2°  C.  Bar.,  74cm.) 

and  free  water  particles  in  the  air. 


taken  during  the  fog 
also  show  the  combined 
effect  of  condensed 
moisture  on  the  cables, 
The  moisture  particles  on 


Kilo-Volts  Effective 

FIG.  136. — Corona  loss  during  fog; 
conductors  wet. 

(Conductor  length,  109,500  cm. 
Diameter,  1.18  cm.  Spacing,  310  cm. 
3/0,7-strand  cable.  Line  A.  Temp., 
2.  Bar.,  75.5.) 


19 

18 
17 
16 
15 
14 
13 

«12 

in 


Kilo-Volts  Eflective 


FIG.  137.  —  Corona  loss  during  snow 
storm. 

(Conductor  length,  109,500  cm. 
Diameter,  1.18  cm.  Spacing,  310cm. 
3/0,7-strand  cable.  Line  A.  Temp., 
0.  Bar.,  74.2.) 


the  conductor  become  charges  and  are  repelled.     The  particles 


CORONA  LOSS 


151 


in  the  air  also  become  charged  and  discharged  thus  increasing  the 
loss  very  greatly  above  that  for  dry  conductors. 

The  losses  during  snow  and  rain  storms  are  much  greater  than 
fair  weather  losses  at  the  same  temperature  and  barometric 


^, 

i 

y 

// 

o^V 

}  y 

/ 

I 

/J 

A" 

f 

> 

/* 

^ 

s^ 

) 

©  — 

—    — 

•9-^ 

^ 

J 

2 

90    100   110    120   130    140    150    160  170    180    190   200   210   220    230 

Kilo  Volts  Effective 

FIG.  138. — Corona  loss  during  sleet  storm. 

(Conductor  length,  109,500  cm.     Diameter,   1.18  cm.     Spacing,  310  cm. 
3/0,7-strand  cable.   Line  A.     Temp.,  -  1.0.     Bar.,  75.4.) 

pressure.  In  Fig.  137  the  actual  measured  loss  is  plotted,  and 
also  a  corresponding  calculated  fair  weather  loss.  The  difference 
between  the  two  curves  shows  the  excess  loss  due  to  snow.  The 
effect  of  snow  is  greater  than  that  of  any  other  storm  condition. 
This  is  because  the  particles 
are  larger  and  a  greater  num- 
ber strike  the  line,  or  come 
near  the  line. 

The  sleet  curves  are  of 
special  interest.  Sleet  had 
already  started  to  form  on 'the 
conductors,  and  was  still  falling 
when  the  tests  were  started. 
Fig.  138  shows  the  loss  curves. 
After  the  curves  were  taken 
the  line  was  kept  at  200,000 
volts  for  over  an  hour  with  no 
apparent  diminution  of  sleet. 
This  seems  to  show  that  sleet 
will  form  on  high-voltage  trans- 
mission lines. 

The  day  after  these  tests  were  made  was  bright  and  clear  and 
the  conductors  were  still  coated  with  sleet.  A  set  of  readings 
was  taken,  and  it  is  interesting  to  note  that  the  excess  loss  here  is 
as  great  as  when  sleet  was  falling.  (See  Fig.  139.) 


FIG. 


Kilo-Volts  Effective 

139. — Corona  loss  with  sleet  on 

the  wires. 

(Conductor  length,  109,500  cm. 
Diameter,  1.18  cm.  Spacing,  310 
cm.  3/0,7-strand  cable.  Line  A. 
Temp.  10.0.  Bar,  76.) 


152 


DIELECTRIC  PHENOMENA 


500 


400 


Curve  Calculated  — 
Points  Measured  X  , 


The  excess  loss  for  sleet,  rain  or  snow  storms  (over  the  fair 
weather  loss)  seems  with  increasing  voltage  to  approach  a  maxi- 
mum and  then  to  decrease  again  (the  latter  at  a  value  very  far 
above  the  disruptive  critical  voltage),  and  the  curves  of  loss  seem 
to  have  the  general  shape  of  the  probability  curve,  as  is  to  be 
expected  theoretically. 

The  above  readings  show  the  im- 
portance of  taking  weather  conditions 
into  account  in  the  design  of  high- 
voltage  transmission  lines. 

Very     High    Frequency. —  Corona 
losses  at  very  high  frequency  are  diffi- 
cult to  measure.     The   curve  in  Fig. 
140  is  interesting.     The  drawn  curve  is 
calculated    from    formula    34  (a) ;    the 
points   are    measured   values.      Power 
was    supplied    from    an    Alexanderson 
100,000-cycle    alternator.     The   power 
FlG'  hi4ghTrequeScyOSSat    was  measured  by  adjusting  reactance 
(Two  parallel  wires,  and  capacity  until  unity  power  factor 
Spacing,  67   cm.    Radius  of  was  obtained.      The  watts  input  was 
wire,  0.127  cm.  /  =  100,000  -.       ., 

~.    Total  length,  200  cm.)  then  the  product  of  volts  and  amperes 
Tests  by  Alexanderson.          as  measured  by  hot  wire  meters. 

This  'good  check  seems  to  show  that  the  formula  applies  over  a 
large  range,  but  complete  conclusions  cannot  be  drawn  from  this 
small  amount  of  data. 


14  16  18  20   22  24  26  28  30 

Kilo-Volts  Eifective.JBetween  Lines 


CHAPTER  VI 


CORONA  AND    SPARK-OVER  IN  OIL  AND  LIQUID  INSULATIONS 

The  most  common  liquid  insulation  is  transformer  oil  obtained 
by  fractional  distillation  of  petroleum.  ,This  oil  has  various 
characteristics,  as  flashing  point,  freezing  point,  viscosity,  etc., 
depending  upon  the  specific  use  to  which  it  is  to  be  put.  The 
average  characteristics  of  transformer  oil  are  as  follows:1 


Medium 

Light 

Flashing  temperature 

180°-  190°  C. 

130°-140°  C 

Burning  temperature  

205°-215°  C. 

140°-150°  C. 

Freezing  point.  .  .                

_10°--15° 

_15°__20°    ' 

Specific  gravity  at  13.5  deg.  C.  .  .  . 
Viscosity  at  40  deg.C.  (Saybolt  test) 
Acid,  alkali,  sulphur,  moisture  .... 

0.865-0.870 
100-110  sec. 
None 

0.845-0.850 
40-50  sec. 
None 

Various  other  oils  are  insulators,  as  gasoline  and  cylinder  oil; 
animal  oils,  as  fish  oil;  vegetable  oils,  as  linseed  oil,  nut  oil,  china 
wood  oil,  etc.  All  of  these  when  pure  have  the  same  order  of 
dielectric  strength. 

The  so-called  compounds  made  by  dissolving  solid  gums  in  oil 
to  increase  viscosity  are  generally  unreliable,  unless  used  dry  as 
varnish.  Under  the  dielectric  field  the  dielectrics  of  different 
permittivities  tend  to  separate,  and  there  is  considerable  loss. 
As  in  air  there  is  very  little  loss  in  pure  oil  until  local  rupture,  that 
is,  brush  discharge  or  corona,  occurs. 

The  dielectric  strengths  of  oils  are  usually  compared  by  noting 
the  spark-over  voltage  between  two  parallel  brass  discs  1.25  cm. 
in  diameter,  and  0.5  cm.  separation.  The  spark-over  voltage  for 
good  oils  in  the  above  gap  should  be  between  50  and  70  kv. 
maximum,  and  hence,  if  the  voltage  wave  is  a  sine,  from  35  to  50 
kv.  effective.2 

Different  Electrodes. — In  Fig.  141  are  plotted  spark-over  curves 
for  different  electrodes  in  good  transformer  oil.  The  character- 

JTobey,  Dielectric  Strength  of  Oil,  A.I.E.E.,  June,  1910. 
2  The  breakdown  voltage  of  oil  like  that  of  air  depends  upon  the  maximum 
point  of  the  wave. 

153 


154 


DIELECTRIC  PHENOMENA 


istics  are  very  much  the  same  as  for  air  excepting  the  apparent 
strength  is  very  much  higher. 

Effect  of  Moisture. — The  slightest  trace  of  moisture  in  oil 
greatly  reduces  its  dielectric  strength.  The  effect  of  moisture 
is  shown  in  Fig.  142 (a)  for  the  standard  disc  gap.  Water  is  held 
in  suspension  in  oil  in  minute  drops.  When  voltage  is  applied 


300 

^ 

cm. 

Sphc 

es  (Dia.) 

26C 

240 
220 
200 

^  180 

/ 

/ 

/ 

X. 

10 
ICn 

:m.  I 
.  Dia 

1SC3 
Oil  I 

ages] 

/ 

y 

/ 

/ 

/ 

y 

X 

1.1 
1>* 

)  cm. 

Sphc 
a.) 

res 

/ 

1 

C-1GO 

I 

// 

^ 

/ 

edles 

£140 
M120 
100 
80 
60 
40 
20 
0 

1 

/s 

I/ 

/ 

/ 

X 

I/ 

7 

^ 

/ 

/ 

r 

1 

/ 

1   / 

? 

(Ter 

ip.  2J 

°o) 

1234         56789      10 
Spacing  cm. 

FIG.  141.  —  Spark-over  of  various  shaped  electrodes  in  oil  at  60  ^. 


these  drops  are  attracted  by  the  dielectric  field.  Thus  they  are 
attracted  to  the  denser  portions  of  the  field  and  may  form  larger 
drops  by  collision.  When  attracted  to,  and  after  touching 
a  metal  part,  and  thus  having  the  same  potential,  they  are  imme- 
diately repelled.  If  the  field  is  uniform  the  drops  form  in  conduct- 
ing chains  along  the  lines  of  force.  It  can  be  seen  that  the  effect 
of  moisture  should  vary  greatly  with  the  shape  of  the  electrode, 
and  with  some  shapes  the  moisture  may  even  be  removed  from 
the  space  between  the  electrodes  by  the  action  of  the  field,  in 
which  case  its  presence  would  not  be  detected  by  low-voltage 
'breakdowns.  In  fact,  for  needle  points  and  most  electrodes 
at  large  spacing  the  breakdown  voltage  for  wet  and  dry  oil  is 
practically  the  same.  In  transformers  moisture  will  generally  be 


CORONA  AND  SPARK-OVER  IN  INSULATIONS 


155 


attracted  to  points  under  greatest  stress.  The  most  effective 
way  of  removing  moisture  is  by  filtration  through  blotting  paper. 
Dirt  in  oil  may  have  an  effect  very  similar  to  moisture  and  the 
small  conducting  particles  be  made  to  bridge  between  electrodes 
by  the  dielectric  field.  Solid  barriers  are  effective  in  preventing 
the  complete  lining  up  of  moisture  particles  between  electrodes. 
While  they  generally  do  not  increase  the  puncture  voltage  for 
dry  oil,  they  very  greatly  increase  reliability  in  apparatus.  See 
page  189.  See  appendix. 

Temperature. — Temperature  over  the  operating  range  has  very 
little  influence  on  the  strength  of  oil.  The  strength  increases  at 
the  freezing  point.  The  curve  is  shown  in  Fig.  142(6).  The 
insulation  resistance  is  also  shown.  The  increase  in  strength 

(a)  (6) 


S  40 
5  30 
o'20 


123456      789     10 
Water-Parts  in  10000  by  Volume 


S    70 
.2     fi0 

\ 

3   bu 

6-C.O 

)lin. 

\ 

fc  o 
io-40 

PQ05 

*- 

^-^ 

k&lfc! 

^\ 

&" 

V 

11  SU 

Ke> 

± 

n 
nee 

J  goU 

^o-20 

S 

5   10 

§      0( 

\ 

N 

)     10   20    30    40    50   60    70   80    90  10 

Oil  Temperature    C° 


FIG.  142. — (a)  Effect  of  water  in  oil.     (6)  Effect  of  temperature  on  di- 
electric strength  and  insulation  resistance.     Tests  at  60  ~. 

with  temperature  is  often  only  apparent  and  due  partly  to  the 
decreasing  insulation  resistance  which  allows  more  current  to 
flow  through  the  oil,  which  tends  to  even  up  the  stress,  but  mostly 
to  the  drying  out  of  moisture  particles  by  the  high  temperature. 
The  increase  at  freezing  should  be  expected,  as  an  actual  improve- 
ment in  dielectric  properties  results.  For  a  perfectly  dry  oil  the 
strength  often  decreases  with  increasing  temperature  or  den- 
sity, as  in  the  case  of  air.  Some  tests  have,  however,  indicated 
an  increase  in  strength  with  temperature. 

The  specific  resistance  of  transil  oil  is  approximately: 
Temp.,  C  Ohms,  cm.  cube. 

30  250  X  1010 

60  100  X  1010 

100  15  X  1010 

The  permittivity  is  approximately  2.6  times  its  specific  gravity 
and  thus  decreases  with  increasing  temperature. 

Spark-over  and  Corona  in  Oil. — A  phenomenon  similar  to 
corona  in  gases  also  takes  place  in  liquid  insulations,  as  oil,  due  to 


156 


DIELECTRIC  PHENOMENA 


a  tearing  apart  of  the  molecules.  Corona  in  oil  is  not  as  steady  or 
definite  as  in  air.  It  appears  to  start  quite  suddenly  and  extend 
much  farther  out  from  the  electrode  than  corona  in  air.  It  is 
much  more  difficult  to  detect  the  starting  point,  and  unless  the 
conductors  are  very  small  or  far  apart  (s/r  large)  corona  does  not 
appear  before  spark-over.  For  instance,  in  the  Table  LXVII 
when  the  outer  cylinder  is  3.81  cm.  radius  and  the  inner  0.0127cm. 
radius  (R/r  =  300)  ,  the  corona  and  spark-over  voltages  are  prac- 
tically the  same  (see  condition  for  spark-over  and  corona,  Chapter 
II).  The  absence  of  corona,  or  rather  the  simultaneous  appear- 
ance of  corona  and  spark-over,  unless  the  wires  are  very  small  or 
far  apart,  seems  to  mean  that  the  mechanism  of  breakdown  in  oil 
is  very  similar  to  that  in  air  but  the  energy  distance  in  oil  is  much 
greater.  Thus,  as  the  voltage  is  increased,  corona  rupture  occurs 
out  to  the  energy  distance;  this  increases  r  to  the  condition  for 
spark-over. 


R 


=  —  <€ 


(r  +  energy  distance  broken  down) 
and    spark   follows.     Therefore,    the    spark-over    voltages    and 

TABLE  LXIV.  —  DIELECTRIC  STRENGTH  OF  No.  6  TRANSIL  OIL  —  SPARK-OVER 
BETWEEN  SPHERES  AT  60  ~ 


Spacing, 
cm. 

Radius  of  spheres,  cm. 

Needles 

0.159 

0.555 

1.27                    3.12 

6.25 

0 

Kv. 
max. 

Gra- 
dient 
max. 
kv./cm. 

Kv. 

max 

Gra- 
dient 
max. 
kv./cm. 

Kv. 
max. 

Gra- 
dient 
max. 
kv./cm 

Kv. 
max. 

Gra- 
dient 
max. 
kv./cm 

Kv. 

max 

Gra- 
dient 
max. 
kv./cm. 

Kv. 
max. 

0.129 
0.198 
0.264 
0.322 

0.378 
0.508 
0.650 
0.766 

1.010 
1.270 
1.780 
2.540 

3.810 
5.080 
7.620 
10.150 

44.6 
50.5 
59.2 
65.0 

71.1 
81.0 

449 
360 
365 
360 

364 
368 

48.0 

394 

47.1 

364 

74.8      289      

73.9 

333 

73.5 

310 

74  .  3      288 

90.0 

295 

107.0      214 

41.6 

99.0 

222 

105.01     220 

89.9 

97.6 
104.0 
111.0 
124.0 

145.0 
168.0 

353 

358 
361 
384 
416 

470 
542 

106.0 

112.0 
116.0 
131.0 
149.0 

172.0 
191.0 

225 

192 
176 
171 
174 

184 
192 

117.0 

187 

128.0 

146.0 
171.0 
203.0 
240.0 

266.0 

182 

166 
158 
137 
122 

103 

132.0 

159.0 
177.0 
214.0 
245.0 

280.0 

180 

166 
147 
130 
110 

90 

157.0 
165.0 
185.0 

206.0 
231.0 

158 
143 
130 

131 
133 

57.0 
84.0 

108.0 
124.0 
166.0 
203.0 

Oil  between  standard  disoa  0.5  cm.  apart  tested  58.5  kv.  max.  25  deg.  C. 


CORONA  AND  SPARK-OVER  IN  INSULATIONS 


157 


TABLE  LXV. — SPARK-OVER  BETWEEN  PARALLEL  PLATES  IN  No.  6  TRANSIL 

OIL  AT  60  ~ 


e  kv. 
max. 

X 
spacing 
cm. 

g'~  1 

kv./cm: 
(max.) 

Remarks 

34.6 

0.254 

136.3 

l\            /FT 

52.3 

0.508 

102.8 

n  pi  fl  I-       . 

71.0 

0.762 

93.0 

^J  Pm(k^' 

106.0 
114.0 
126.5 

1.015 
1.270 
1.525 

104.8 
89.6 
82.8 

Distance  between  small  and  large  discs  = 
0.476  cm. 

125.2 

1.270 

98.2 

• 

137.5 

1.525 

90.0 

158.0 

1.778 

85.0 

167.7 

2.03 

82.2 

187.3 

2.29 

81.8 

Same  as  above,  except  distance  between 

small  and  large  discs  =  1.58  cm. 

196.5 

2.54 

77.2 

214.5 

2.79 

76.6 

225.0 

3.05 

74.0 

242.0 

3.30 

73.2 

113.2 

1.27 

88.8 

155.5 

2.54 

61.0 

4-in.  flat  discs,  0.5-cm.  radius  edge. 

212.0 

5.08 

41.7 

% 

269.0 

7.62 

35.0 

TABLE  LXVI. — CORONA  IN  OIL,  WIRE  AND  PLATE 
(Distance  of  wire  from  plate  =  16.5  cm.  at  60  ~) 


Kv.  eff. 

Radius  wire,  cm. 

0i 
kv./cm.  eff. 

o* 

kv./cm.  max. 

50 

0.025 

278 

393 

60 

0.050 

185 

262 

80 

0.0635 

201 

284 

100 

0.1520 

122 

173 

55 

0.00508 

615 

870 

158 


DIELECTRIC  PHENOMENA 


corona  voltages  up  to  fairly  high  ratios  of  R/r  are  the  same,  and 
may  be  used  in  determining  the  strength  of  oil. 

TABLE  LXVIL — SPARK-OVER  VOLTAGES  FOR  No.   6   TRANSIL  OIL  CON- 
CENTRIC CYLINDERS 


R  cm. 

r  cm. 

Kv.  eff. 

Kv.  max. 

gg  max. 

1 

R 

Remarks 

kv./cm. 

Vr 

r 

3.81 

0.032 

45.3 

64.0 

420.0 

5.61 

120.00 

Tests    made    in 

3.81 

0.238 

60.0 

84.8 

127.7 

2.05 

16.00 

long     cylinders 

3.81 

0.317 

60.5 

85.5 

108.1 

1.77 

12.00 

with    belled 

3.81 

0.635 

69.5 

98.3 

86.3 

1.26 

6.00 

ends.     Oil    be- 

3.81 

0.794 

75.0 

106.1 

85.5 

1.12 

4.80 

tween  standard 
discs    0.5     cm. 

3.81 
3.81 
3.81 

0.952 
1.111 
1.270 

73.0 
76.7 
76.0 

103.2 
108.5 
107.5 

78.1 
79.4 
77.0 

1.02 
0.95 
0.89 

4.00 
3.00 

apart  tested  58 
kv.    (max.)    25 
deg.  C. 

3.81 

1.587 

73.7 

104.3 

75.1 

0.79 

2.40 

3.81 

1.905 

66.3 

93.7 

70.7 

0.72 

2.05 

3.81 

2.540 

45.5 

64.3 

62.4 

0.63 

1.57 

6.67 

5.560 

29.2 

41.3 

40.6 

Tests    made    on 

6.67 

5.080 

43.7 

61.8 

44.8 

short  cylinders 

6.67 

3.970 

70.1 

99.2 

48.1 

where    field    is 

6.67 

3.240 

84.4 

119.5 

51.0 

somewhat    dis- 

6.67 

2.230 

105.8 

149.7 

61.2 

torted. 

6.67 

1.955 

105.0 

148.5 

61.9 

6.67 

1.615 

103.5 

146.5 

64.0 

6.67 

1.270 

101.3 

143.2 

67.5 

6.67 

0.953 

98.3 

139.0 

75.0 

6.67 

0.635 

94.0 

133.0 

89.2 

• 

6.67 

0.477 

91.5 

129.5 

102.8 

6.67 

0.318 

85.3 

120.7 

121.0 

6.67 

0.159 

65.2 

92.2 

155.5 

6.67 

0.079 

62.2 

88.0 

251.4 

11.42 

3.930 

144.0 

203.5 

48.3 

11.42 

2.280 

163.0 

230.4 

63.0 

11:42 

1.910 

158.0 

223.2 

64.5 

11.42 

1.270 

160.0 

226.0 

81.5 

11.42 

0.880 

148.0 

209.0 

93.0 

11.42 

0.520 

90.0 

127.3 

79.5 

The  strength  of  oil  for  different  sizes  of  wire  from  Table  LXVII 
is  plotted  in  Fig.  143.  The  curve  is  similar  to  that  for  corona  in 
air.  Fig.  144  shows  that  a  straight  line  relation  holds  approxi- 


CORONA  AND  SPARK-OVER  IN  INSULATIONS 
1 


159 


mately  between  —7=  and  gv.     Values  are  not  used  when  R/r  >  3.5. 
Thus,  as  in  the  case  of  air:1 


gv  =  36 


/          !-2\ 
(1  +  "~7=lkv. 


/cm.  max. 


1.2 


. 

gv  =  25.51  1  -f-  —7=  I  kv./cm.  effective  sine  wave. 
vr 


200 

180 
J160 
1 140 

120 

> 

I 
,  80 

60 
40 
20 


.4 


.8 


1.2         1.6        2.0 

Badius-cm. 


2.4 


2.8        3.2 


FIG.  143.— Strength  of  oil  at  60  ~, 
(Concentric  cylinders — gv  at  surface  of  inner  cylinder.) 


•JQ 
180 
.160 

w'120 
S  100 

t  80 

S»   60 
40 
20 

^ 

^ 

^ 

•^ 

P^l 

-^ 

^ 

^ 

"^^ 

^ 

<f 

^ 

^ 

- 

^ 

"^^ 

8    1.2    1.6  1  2.0   2.4   2.8    3.2   3.6 

FIG.  144. — Strength  o£  oil  at  60  ~. 
(Method  of  reducing  values  given  in  Fig.  143  to  equation.) 

The  energy  distance  is  1.2\/r  or  almost  four  times  that  of  air, 
indicating  that  a  greater  amount  of  energy  is  required  to  rupture 
oil,  or  a  greater  number  of  collisions  are  necessary  before  ionic 

1  F.  W.  Peek,  Jr.,  High  Voltage  Engineering,  Journal  Franklin  Institute, 
Dec.,  1913. 


160 


DIELECTRIC  PHENOMENA 


saturation  is  reached.  g0  and  a  vary  to  a  considerable  extent  in 
oil.  The  strength  of  oil,  or  the  disruptive  gradient,  or  the  gradi- 
ent required  to  bring  the  ions  up  to  collision  velocity,  seems  fairly 
low.  Oil  should,  therefore,  have  low  strength  in  bulk,  but  high 


700 

^600 
1*500 
S400 
^300 

f00 

^100 


01234 
Spacing  cm. 

FIG.  145. — Showing  increase  of  strength  of  oil  at  small  spacings  at  60 
(Spheres,  R  =  3.33cm.) 


300 
340 

320 

300 

280 

260 

S*220 

'.  200 

>    < 
M  160 

5  140 

*120 

\ 

100 

^ 

^ 

80 

*^-. 

---. 

"*»-^ 

fiO 

-  — 

•—-  - 

-  — 



-»-. 

20 

1  2  3  4   5  6  7  8   9  10  11  12  13 

Eadius- 

FIG.  146. — Strength  of  oil  between  spheres  at  60  ~. 
(Data  from  constant  part  of  the  curve.) 

apparent  strength  when  sub-divided  or  confined  to  make  use  of 
the  large  energy  distance  necessary  to  rupture. 

Spark-over  voltages  and  gradients  are  given  for  various  spheres 


CORONA  AND  SPARK-OVER  IN  INSULATIONS 


161 


at  various  spacings  in  Table  LXIV.  The  characteristics  of  the 
curves  between  gradient  and  spacing  are  the  same  as  those  for 
air  (see  Fig.  42)  as  shown  in  Fig.  145.  When  the  spacing  is  so 
small  that  it  interferes  with  the  energy  distance  the  apparent 
strength  of  oil  increases.  At  spacings  above  this  the  gradient 
is  constant  until  the  separation  is  so  great  that  corona  forms 
before  spark-over. 


TABLE  LXVIII. — SPHERES  IN  OIL 
Gradient  at  constant  part  of  the  curve.     Tests  at  60 
Data  from  Table  LXIV 


Radius,  cm. 

Gradient, 
kv./cm.  max. 

1 

VR 

Radius,  cm. 

Gradient, 
kv./cm.  max. 

l 

VR 

0.159 

348 

2.51 

1.27 

120 

0.89 

0.237 

260 

2.05 

3.12 

98 

0.56 

0.355 

222 

1.68 

6.25 

82 

0.40 

0.555 

169 

1.35 

12.50 

56 

0.28 

The  rupturing  gradient  at  the  constant  part  of  the  curve  for 
various  spheres  is  given  in  Table  LXVIII,  and  is  shown  in  Fig. 
146.  This  may  be  written  approximately 

/  4    \ 

g,  =  28.3    1  +  -7-     kv./cm.  max. 


The  energy  distance  is  approximately 

The  spark-over  voltages  for  concentric  cylinders,  where  R/r  < 
about  5,  and  for  spheres  above  2\/R  spacing  on  the  constant 
part  of  the  curve,  may  be  approximated  by  substituting  g  in  the 
voltage  formula 


r> 

e  =  gvr  loge  —  cylinders 

X 

e  =  g  -     spheres 


(use  gv,  p.  159) 
(use  g,  above) 


In  oil,  the  apparent  strength  can  be  greatly  improved  by  limiting 
the  free  energy  distance  by  barriers,  etc.  This  can  be  seen  in 
Tables  LXIV  and  LXV,  where  e/X  is  given  for  parallel  planes, 
and  gv  for  spheres.  For  the  small  spacings,  where  the  free  energy 
distance  is  limited,  the  apparent  rupturing  gradient  is  very  high, 


162 


DIELECTRIC  PHENOMENA 


just  as  in  the  case  of  air.  Strengths  as  high  as  700  kv./cm.  have 
been  reached.  Insulation  barriers  give  an  added  effect  by  pre- 
venting moisture  particles  from  lining  up. 

Care  must  be  taken,  however,  that  the  barriers  are  not  so 
placed  as  to  increase  the  stress  on  the  oil  by  the  high  permit- 
tivity of  the  solid  insulation. 

Transient  Voltages. — Transient  voltages  or  impulse  voltages  of 
short  duration  greatly  in  excess  of  the  low  frequency  rupturing 
voltages  may  be  applied  to  insulations  without  rupture.  In 
other  words,  the  rupture  of  insulation  requires  not  only  a  suf- 

(«) 


? 


Above  circuit  used  by  author.  A  is  sparked-over 
by  transformer  voltage.  C  then  discharges  through 
L,  arc  at  A,  and  R.  Impulse  appears  across  R,  at  I. 
The  power  arc  at  A  is  non-oscillatory  and,  in  effect, 
a  switch.  The  impulse  voltage  is  determined  by  C, 
L  and  R. 


FIG.  147. — "Impulse"  circuits. 

ficiently  high  voltage,  but  also  a  definite  minimum  amount  of 
energy.  This  means  also  that  a  definite  but  very  small  time 
elapses  between  the  application  of  voltage  and  breakdown. 
This  is  sometimes  called  the  "dielectric  spark  lag"  and  has 
already  been  discussed  for  air  in  Chapter  IV.1  The  rupturing 
energy  seems  to  be  much  greater  for  oil  than  for  air,  as  indicated 
by  the  large  energy  distance  in  the  gradient  equation  above. 
At  low  frequency  a  given  definite  voltage  is  required  to  cause 
1  Peek,  "The  Effect  of 'Transient  Voltages  on  Dielectrics,"  A.I.E.E. 
Trans.,  1915,  page  1857. 


CORONA  AND  SPARK-OVER  IN  INSULATIONS 


163 


rupture  during  the  comparatively  unlimited  time  of  application. 
This  voltage  is  constant  until  the  application  is  limited  to  a 
definite  minimum  time,  when  a  higher  voltage  is  required  to 
accomplish  the  same  results  in  limited  time.  Such  transient 
voltages  of  short  duration,  and  impulses  of  steep  wave  front, 
must  not  be  confused  with  continuously  applied  high  frequency 
where  breakdown  will  generally  take  place  at  lower  voltages, 
due  to  loss,  etc. 

In  Table  LXIX  the  relative  breakdown  voltages  of  gaps  in  oil, 
at  60  cycles,  and  for  impulse  voltages  of  steep  wave  front,  are 
given.  An  impulse  voltage  much  higher  than  the  60-cycle  vol- 
tage is  required  to  break  down  a  given  gap.  If  similar  air  and  oil 
gaps  are  set  to  rupture  at  the  same  low  frequency  voltage,  a  much 
higher  transient  voltage  will  be  required  to  rupture  the  oil  gap 
than  the  air  gap,  indicating  greater  time.  An  air  gap  may  thus 
protect  an  oil  gap,  but  not  vice  versa.  See  page  108  and  appendix. 

TABLE  LXIX. — COMPARISON   OF   GO-CYCLE  AND  IMPULSE    SPARK-OVER  IN 

OIL  AND  IN  AIR 


Oil 

Air 

Gap 

Spacing, 
cm. 

Kv.  60 
cy.,  max. 

Kv.  im- 
pulse, 

Gap 

Spacing, 
cm. 

Kv.  60 
cy.,  max. 

Kv.  im- 
pulse, 

max. 

max. 

Stand,  disc.  .  .  . 

0.5 

56.6 

170.0 

• 

2/0  needles  .  .  . 

1.0 

50.2 

103.3 

2/0 

5.1 

50.2 

67.8 

2.0 

68.8 

157.0 

needles 

17.5 

108.0 

198.0 

3.0 

89.2 

233.3 

4.0 

108.0 

321.0 

0.25 

37.2 

117.3 

2.54-cm. 

0.51 

62.8 

199.4 

spheres. 

0.77 

87.5 

279.0 

1.02 

111.2 

337.0 

6.25-cm. 

0.25 

47.5 

162.5 

spheres. 

0.51 

68.3 

244.5 

0.70 

88.3 

267.0 

1.02 

115.8 

284.0 

The  above  voltages  are  measured  by  sphere  gaps  at  low  fre- 
quency and  for  impulse.  The  difference  between  the  60  cycles 
and  impulse  voltages  increases  as  the  steepness  of  the  im- 
pulse increases.  Fig.  147  shows  impulse  circuits.  Fig.  147(6), 


164 


DIELECTRIC  PHENOMENA 


8.4 
8.0 
7.6 

6.8 
6.4 
6.0 

5.2 
4.8 
4.4 
S4.0 
3.6 
3.2 
2.8 
2.4 
2.0 
1.6 

0.8 
0.4 

0 

\ 

\ 

00 

1 

1 

^ 

I 

X 

X4.( 

0 

1 

/ 

. 

1 

/ 

X 

^3.00 

/ 

/ 

/ 

1 

7 

/ 

/ 

^ 

^ 

"2. 

00 

1 

1 

s 

X 

/ 

/ 

^ 

/ 

1  / 

/ 

• 

JO 

1, 

1 

// 

^ 

-^" 

I// 

2 

r 

. 

f 

"^"^ 

^ 

s» 

3    10    20    30  40   50   60   70   80    90  1001] 
Kilo  -Volts 

FIG.  148.  —  Needles  in  air. 

2.1 

2.0 
1.9 
1.8 
1.7 
1.6 
1.5 
1.4 
1.3 
1.2 
1.1 
S1.0 
0.9 
0.8 
0.7 
0.6 
0.5 
0.4 
0.3 
0.2 
0.1 
0 


1.0 


2.0 


1.0 


3.0 


0    10  20  30    40  50    60    70   80   90  100110 
Kilo-VoHs 

FIG.  149. — Spheres  in  air. 


(Transient  voltages.    Limited  energy.) 


0  10  20  30  40  50  60  70  80  90  100 
Kilo -Volts 


U.4U 

0.38 
0.36 
0.34 
0.32 
0.30 
0.28 
0.26 
0.24 
0.22 
§0.20 
0.18 
0.16 
0.14 
0.12 
0.10 
0.08 
0.06 
0.04 
0.02 

0 

\l 

/ 

/ 

/ 

/ 

00 

/ 

/ 

/ 

/ 

1 

1 

^ 

-^ 

4.0 

I 

^ 

^ 

" 

I 

/ 

^^~ 

-  — 

^  — 

2.0 

/ 

/ 

^ 

•^ 

• 

1 

// 

/ 

^, 

^ 

-^^-" 

1 

% 

s^~ 

/* 

—  — 

= 

—  i 

.50 

E=  

£ 

0  10  20  30  40  50  60  70  80  90  100 
Kilo -Volts 


FIG.  150. — Needles  in  oil.  FIG.  151. — Spheres  in  oil, 

(Transient  voltages,    Limited  energy,) 


CORONA  AND  SPARK-OVER  IN  INSULATIONS 


165 


however,  does  not  give  a  circuit  for  which  the  constants  can  be 
definitely  calculated.  Oil  is  an  excellent  insulation  in  combina- 
tion with  barriers.  On  solid  insulations  the  effect  of  transient 
voltages  is  cumulative.  A  partial  break  occurs  which  is  en-  v 
larged  by  each  succeeding  impulse,  until  finally  dynamic  follows. 
With  oil,  such  "  cracks"  are  closed  up  by  new  oil  immediately. 

One  investigation  shows  that  when  the  energy  is  limited  a 
voltage  is  reached  where  the  spark  distance  becomes  a  function  of 
the  energy  and  practically  independent  of  the  voltage.1  Figs. 
148,  149,  150,  151  taken  from  this  investigation  show  the  spark- 
over  curves  for  oil  and  air.  The  figures  on  the  curves  represent 
the  current  allowed  to  enter  in  the  impulse,  and  thus  indirectly 
indicate,  to  a  certain  extent,  the  energy.  The  impulse  was 
produced  by  suddenly  applying  a  continuous  voltage  to  the  low 
side  of  a  transformer  (Fig.  1476).  The  curve  marked  «>  is  for 
infinite  energy  supply  (60  cycles) .  If  sphere  gaps  are  set  in  air 
and  in  oil  for  30  kv.  at  60  cycles  the  spacings  are  0.95  cm.  and  0.16 
cm.  respectively.  If  a  transient  voltage  of  100  kv.  is  applied, 
the  gap  in  oil  will  not  spark  over  if  the  energy  applied  to  the 
circuit  is  less  than  1.04  joules  (4  amp.).  For  air  the  minimum 
energy  is  0.45  joule  (1.5  amp.). 

At  continuously  applied  high  frequency  oil  breaks  down  at 
lower  voltages  than  at  60  cycles.  The  following  comparison 
made  by  the  author  is  of  interest. 

TRANSIL  OIL — BETWEEN   FLAT  TERMINALS — SQUARE    EDGE — 2.5-CM.   DI- 
AMETER— 0.25-CM.   SPACE — BREAKDOWN  VOLTAGE   GRADIENTS 


60  cycles 

High  frequency 
alternator 
90,000  cycles 

Single  impulse,  sine 
shape,  corresponding  to 
200,000  cycles 

Kv./mm. 
(max.) 

Kv./mm. 
(max.) 

Kv./mm. 
(max.) 

17 

6.7 

39 

D.C.  Strength  of  Oil.2 — The  d.c.  strength  of  oil  generally 
corresponds  to  the  maximum  (\/2  X  effective)  60  ~  value. 

1  Hayden  and  Steinmetz,  Transactions  A.I.E.E.,  June,  1910. 

2  Peek,  "  The  Effect  of  High  Continuous  Voltages  on  Air,  Oil  and  Solid 
Insulation,"  A.I.E.E.,  1916. 

11 


v 


CHAPTER  VII 
SOLID  INSULATIONS 

General. — Some  of  the  principal  solid  insulations  are  varnished 
cambric,  oiled  and  varnished  pressboard,  built  up  pressboard, 
treated  wood,  mica,  micanite,  soft  and  hard  rubber,  synthetic 
resins,  glass,  and  porcelain. 

With  gaseous  and  liquid  insulations  as  air  and  pure  oil  there  is 
very  little  loss  up  to  the  breakdown  gradient.  A  gradient  just 
under  the  breakdown  gradient  may  be  applied  and  held  and  the 
loss  is  so  small  that  no  appreciable  heating  results.  Thus,  the 
loss  in  air  and  oil  is  essentially  a  phenomenon  above  the  electric 
elastic  limit.  This  loss  generally  exists  in  some  locally  broken 
down  part  of  the  insulation,  as  the  corona  on  the  surface  of  a  wire. 
The  break  does  not  extend  through  the  whole  insulation,  and 
when  the  stress  is  removed,  new  air  takes  the  place  of  the  broken 
down  air  and  all  evidence  of  overstress  is  removed ;  in  other  words, 
in  air  and  oil  a  local  breakdown  is  "self  healing." 

Almost  all  insulations  are  partially  conducting  or  have  a  very 
high  resistance  which  is  spoken  of  as  insulation  resistance.  The 
actual  resistance  of  the  insulation  itself,  which  is  very  high, 
apparently  has  no  direct  connection  with  the  dielectric  strength, 
which  is  measured  by  the  gradient  or  flux  density  or  stress  re- 
quired to  electrically  strain  the  dielectric  above  the  "electrical 
elastic  limit"  so  that  actual  rupture  or  breakdown  occurs.  For 
instance,  in  a  condenser  made  of  two  metal  plates  with  a  solid 
dielectric  between  them,  when  a.c.  potential  is  applied,  energy 
is  stored  in  the  dielectric  by  electric  displacement  at  increasing 
potential  and  delivered  back  to  the  circuit  at  decreasing  potential, 
as  long  as  the  potential  does  not  stress  the  insulation  above  the 
elastic  limit.  If  the  dielectric  were  perfect  a  wattmeter  in  the 
circuit  would  indicate  no  loss.  In  all  practical  insulations  the 
wattmeter  does  read  a  loss  due  to  the  PR  loss  in  the  insulation, 
and  the  dielectric  loss,  sometimes  called  dielectric  hysteresis.1 
If  the  voltage  is  sufficiently  increased  to  exceed  the  elastic 
limit  actual  rupture  or  breakdown  occurs;  along  this  discharge 
path  the  insulation  is  destroyed.  Air  has  a  very  high  insulation 

1  In  what  follows  the  total  loss  will  be  called  the  dielectric  loss.  See 
pages  36,  37. 

166 


SOLID  INSULATIONS 


167 


resistance,  but  not  a  very  high  dielectric  strength.  When 
the  insulation  resistance,  however,  of  a  given  solid  insulation 
becomes  very  low,  as  caused  by  moisture,  etc.,  it  is  an  indica- 
tion of  large  loss  and  low  breakdown  voltage.  Thus,  the  term 
" insulation  resistance"  generally  takes  into  account  the  resist- 
ance of  the  occluded  moisture. 

Insulation  Resistance. — The  actual  resistance  of  the  insulating 
material  itself  is  generally  very  high.  Practically  all  solid  and 
liquid  insulations  absorb  moisture  to  a  greater  or  less  extent. 
The  capillary  tubes  and  microscopic  interstices,  etc.,  in  the  struc- 
ture become  rilled  with  moisture  and  gases.  In  the  non-homo- 
geneous structure  this  makes  a  complicated  arrangement  of  ca- 
'(«)  (6). 


FIG.  152. — Diagrammatic    representation    of    resistance    arrangement    in 
imperfect  insulations 

parities  and  resistances  in  series  and  in  multiple.  A  simplified 
diagrammatic  illustration  of  the  distribution  is  shown  in  Fig.  152. 

Let  152 (a)  represent  a  magnified  section  of  insulation  between 
two  terminals,  and  152(6)  a  diagrammatic  representation.  The 
resistance  of  the  insulation  itself,  which  is  very  high,  may  be 
represented  by  rt-.  1  may  be  a  moist  fiber  which  extends 
only  partially  through  the  insulation  and  is  thus  in  series  with 
a  capacity.  It  may  be  represented  by  ra.  3  and  4  may  be 
wet  fibers  which  extend  all  the  way  across,  and  are  represented 
by  rm.  There  may  also  be  leakage  resistance  over  the  surface. 

Direct  current  is  used  to  measure  insulation  resistance,  as  the 
charging  current  for  a.c.  is  very  large  and  masks  the  resistance 
current.  Watt  measurements  are  necessary,  as  well  as  volts  and 
amperes,  to  determine  the  effective  a.c.  resistance.  The  a.c.  and 


168 


DIELECTRIC  PHENOMENA 


d.c.  resistance  should,  however,  be  quite  different.  When  d.c. 
is  used  sufficient  time  must  elapse  after  the  application  of  voltage 
to  allow  for  absorption  (see  Chapter  II,  page  36). 

With  d.c.  the  only  path  for  the  current  is  through  r<  and  rm  in 
multiple,  which  is,  therefore,  the  resistance  measured.  The 
resistance  varies  with  the  applied  potential,  decreasing  with  in- 
creasing potential.  The  conducting  particles  are  caused  to  line 
up,  cohere,  occluded  gases  break-down,  etc.,  as  the  potential  is 
increased. 

When  a.c.  voltage  is  applied  to  insulation  the  capacity  current 
must  pass  through  ra;  in  shunt  with  this  is  the  circuit  through 
Ti  and  rm.  The  loss  in  ra  must  increase  with  increasing  frequency, 
while  the  loss  through  r»  and  rm  must  remain  constant  at  a  given 
voltage,  independent  of  the  frequency.  The  greater  loss  will 
generally  occur  in  ra.  The  d.c.  insulation  resistance  cannot  be 
used  in  approximating  the  Pr  a.c.  loss.  If  the  a.c.  loss  is  meas- 
ured, as  well  as  the  voltage  and  current,  the  effective  resistance 
may  Ije  calculated.  This  resistance  loss,  however,  must  be 
greater  than  that  due  to  ra  as  other  losses  are  included. 

In  Table  LXX  some  d.c.  resistances  are  given  for  different 
materials.  Note  the  effect  of  moisture  absorbed  from  the  air 
even  for  varnished  materials. 

TABLE  LXX. — INSULATION  RESISTANCE 

Resistance  Megohms  per  Cm.  Cube 
(Data  obtained  by  Evershed,  J.I.E.E.,  Dec.  15,  1913) 


D.c. 

volts 

50 

100 

200 

500 

Cotton,  dry  

350.0 

275.0 

200  0 

140 

Cotton,  not  dried 

2  8 

2  5 

2  2 

Micanite,  exposed  to  air  
Micanite,  dried  

220.0 

175.0 

160.0 
300,000 

140 

200,000 

Cylinder  oil,  trace  of  moisture 
Cylinder  oil   dry 



22,000 
36,000 

22,000 
36,000 

22,000 
36,000 

Varnished  cloth,  12  hr.  after 

35,000 

35,000 

35,000 

baking.    ' 
Varnished  cloth,  9  days  after 
baking. 

17,000 

14,000 

11,000 

9,000 

SOLID  INSULATIONS 


169 


With  air  and  oil  an  appreciable  loss  begins  only  when  a  definite 
gradient,  sufficiently  large  to  cause  local  rupture  as  brush  or 
corona,  somewhere  results;  loss  occurs  after  the  elastic  limit  has 
been  exceeded.  The  dielectric  loss  in  solid  dielectrics  is  essen- 
tially a  loss  below  the  elastic  limit.  In  solid  dielectrics  a  stress 
may  be  applied  lower  than  the  elastic  limit,  which  after  a  short 
time — on  account  of  the  heating  and  hence  weakening  of  the 
insulation — will  cause  rupture. 

Rupturing  Gradients. — Apply  voltage  lower  than  the  puncture 
voltage  between  concentric  cylinders  with  dry  insulation  between 
surfaces,  and  gradually  increase  to  the  rupturing  voltage  within  a 
short  time  so  that  there  can  be  no  appreciable  rise  in  temperature. 
The  mechanism  of  rupture  will  be  quite  different  for  oil  or  air,  glass 
or  porcelain,  and  cambric.  For  oil  and  air  corona  results  near  the 
surface  of  the  inner  cylinder,  the  breakdown  is  local,  and  disappears 


100 


15          20  25 

Time  Minutes 


30 


35 


FIG.   153. — Insulation  puncture  voltage  vs.  time. 

(Oiled  pressboard,  2.5  mm.  thick.     The  curve  does  not  cut  the  kv  axes  as 
it  appears  to  on  account  of  the  time  scale.) 

when  the  stress  is  removed;  or,  if  the  stress  is  further  increased 
spark-over  finally  results.  For  glass  or  porcelain,  as  soon  as  over- 
stress  is  reached  locally,  a  crack  results  at  the  surface  of  the  inner 
cylinder  and  complete  breakdown  follows.  With  cambric  there 
is  local  rupture  and  local  charring  of  the  insulation,  which  forms 
carbon  " needles. "  The  break  is  progressively  increased;  this 
continues  until  the  breakdown  is  complete.  A  wet  thread  or 
gas  bubble,  as  (1)  in  Fig.  152 (a),  may,  in  effect,  act  as  a  needle 
and  thus  cause  breakdown.  The  breakdown  gradients  of  solid 
insulations  are  thus  variable  and  not  as  definite  as  with  air  and  oil. 
The  puncture  tests  on  solid  insulations  vary  greatly  between 
different  samples  of  the  same  material,  shape  and  area  of  the 
electrodes,  time  of  application  of  voltage,  etc.  Insulations  should 
be  thoroughly  dried  before  tests  are  made. 


170 


DIELECTRIC  PHENOMENA 


In  comparing  solid  insulations  it  is  generally  best  to  make  some 
arbitrary  time  tests  to  include  the  effect  of  dielectric  loss,  and 
thus,  heating  on  the  breakdown  voltage.  The  effect  of  loss  is 
cumulative;  the  insulation  becomes  warm  and  while  the  loss 
increases  with  the  temperature,  the  dielectric  strength  generally 
decreases  with  increasing  temperature.  The  ultimate  strength 
naturally,  then,  depends  on  the  rate  at  which  this  heat  is  con- 
ducted away.  This  is  illustrated  in  Fig.  153.  With  the  electrode 
used,  if  the  voltage  is  " rapidly  applied"  before  heating  occurs, 
80  kv.  are  required  to  cause  rupture.1  If  50  kv.  are  applied 
rupture  does  not  occur  until  4  minutes  have  elapsed,  while  30  kv. 
may  be  applied  indefinitely  without  rupture  if  the  room  tem- 
perature is  not  increased.  The  curve  does  not  cut  the  voltage 
axes  as  appears  in  the  cut,  on  account  of  the  time  scale,  but  is  an 
asymptote  to  it.  The  effect  of  temperature  is  also  illustrated  in 
Table  LXXI,  where,  in  one  case,  the  electrode  is  of  brass  giving 
good  heat  conduction,  and  in  the  other  case  of  wood  coated  with 
tin-foil  giving  poor  heat  conduction.  As  the  applied  voltage 
approaches  the  "rapidly  applied"  rupturing  voltage  there  is  not 
sufficient  time  for  the  insulation  to  heat  to  a  great  extent  and  the 
effect  is  about  the  same  for  either  brass  or  the  coated  wood 
electrode.  The  effect  of  heating  is  also  shown  by  d.c.  tests, 
page  191. 

TABLE  LXXI. — EFFECT  OF  HEAT  CONDUCTING  PROPERTIES  OF 
TERMINALS  ON  TIME  OF  BREAKDOWN 

Two  Thicknesses  of  No.  12  Oiled  Cloth 
(From  Rayner,  Journal  I.E.E.,  Feb.  8,  1912) 


Time  of  breakdown 

Brass  terminals 

Wood  terminals2 

9,000 

570  .  0  sec. 

50.0  sec. 

10,000 

48  .  0  sec. 

19.0  sec. 

11,000 

16.5  sec. 

10.0  sec. 

12,000 

10.2  sec. 

6.2  sec. 

14,000 

5.2  sec. 

4  .  5  sec. 

1  Rapidly  applied  voltage  as  used  above  means  voltage  applied  within  a 
fairly  short  time,  a  few  seconds,  and  not  impulse  voltage  or  voltage  of  very 
steep  wave  front.     "Instantaneous"  is  commonly  used  to  designate  this 
test;  this  term  is  confusing.     The  test  itself  is  not  wholly  satisfactory  as 
it  is  indefinite.     It  offers,  however,  a  means  of  making  a  preliminary  com- 
parison of  insulations. 

2  Coated  with  tin-foil. 


SOLID  INSULATIONS 


171 


The  effect  of  applying  a  high  voltage,  allowing  different  periods 
of  rest  for  cooling,  and  then  applying  voltage  until  rupture,  is 
shown  in  Table  LXXII.  The  injurious  effects  of  applying  high 
voltage  for  different  lengths  of  time  is  shown  in  Table  LXXIII. 
This  is  probably  due  to  the  effect  of  heat  and  injury  to  the  sur- 
face by  corona. 

TABLE  LXXII. — RECOVERY  IN  VARYING  PERIODS  OF  REST  AFTER  APPLI- 
CATION OF  9000  VOLTS  FOR  1  MINUTE l 

Two  Thicknesses  of  No.  12  Oiled  Cloth 
(From  Raynor,  Journal  I.E.E.,  Feb.  8,  1912) 


Period  of  rest 

Time  to  break  at 
11,000  volts 

Period  of  rest 

Time  to  break  at 
11,000  volts 

0.  . 

2  6  sec. 

o 

2  5  sec. 

1  min  

9.5  sec. 

5  sec. 

4.4  sec. 

2  min  

119  sec. 

15  sec. 

9  0  sec. 

Fresh  material.  .  .  . 

12.0  sec. 

60  sec. 
Fresh  material 

9.8  sec. 
20  5  sec. 

TABLE  LXXIII 
(From  Raynor,  Journal  I.E.E.,  Feb.  8,  1912) 


Time  of  treatment  at 

Time  of  breakdown  ( 

left  to  cool  over  night) 

5000  volts 

At  6500  volts 

At  7000  volts 

0 

22  0  min 

8  5  min 

1  hr  

6  5  min. 

8  3  sec. 

2  hr 

3  0  sec. 

TABLE  LXXIV. — EFFECT  OF  AIR  GAP  (CORONA) 
Two  Thicknesses  of  No.  12  Oiled  Cloth 

10,000  Volts 
(Raynor,  Journal  I.E.E.,  Feb.  8,  1912) 


Air  gap,  mm. 


0.00 
0.30 
0.50 
0.75 
1.05 


Time   to   puncture, 
seconds 


42.0 
34.0 
27.5 
24.0 
120  (irregular) 


1  Time  to  break  at  9000  volts,  1-4*  to  2  minutes. 


172 


DIELECTRIC  PHENOMENA 


The  action  of  corona  or  breakdown  of  the  air  at  the  surface  of 
the  insulation  is  shown  in  Table  LXXIV. 

The  arbitrary  practical  tests  for  comparing  insulations  are  the 
Rapidly  Applied  (Instantaneous)  Test,  the  One-minute  Test, 
and  the  Endurance  Test.  Rapidly  applied  breakdown  voltage 
is  found  by  applying  a  fairly  low  voltage  and  rapidly  increasing 
until  breakdown  occurs.  Voltage  should  be  increased  at  about 
5  kv.  per  sec. 

The  Minute  Test  is  made  by  applying  40  per  cent,  of  the  rapidly 
applied  voltage,  and  increasing  this  voltage  10  per  cent,  at  1- 
minute  periods  until  puncture  occurs.  (Total  time  about  5  min.) 

The  Endurance  Test  is  made  by  applying  40  per  cent,  of  the 
minute  test  voltage  and  increasing  the  voltage  10  per  cent,  every 
hour  or  half  hour  until  puncture  occurs.  These  tests  may  be 
made  at  any  given  temperature.  The  electrode  should  be  of  a 
given  size  and  weight.  Ten-centimeter  diameter  electrodes, 
slightly  rounded  at  the  edges,  will  be  found  convenient.  Table 
LXXV  gives  an  example  of  such  tests. 

TABLE  LXXV 

Muslin  with  Three  Coats  Varnish — Total  Thickness  2  mm. 
Rapidly  Applied  (Instantaneous)  Breakdown  and  Resistance 


Temp.,  deg. 

Resistance  in  megohms  for  samples 

cent. 

1 

2 

3 

4 

5 

20 

73,400 

73,400 

97,900 

97,900 

73,400 

75 

650 

390 

310 

270 

170 

100 

100 

90 

73 

70 

50 

Breakdowns  in  kilovolts.     Tests  made  in  oven  at  100°  C. 


100 

40.6 

42 

44 

43 

36.5 

Average  breakdown  40.6  kilovolts 


One-minute  Test 

Apply  40  Per  Cent,  of  Rapidly  Applied  Breakdown  Voltage  for  1  Minute, 
with  10  Per  Cent.  Increase  in  Voltage  Each  Minute 


Resistance  in  megohms 

Temp.,  deg. 

cent. 

6 

7 

8 

9 

10 

20 

73,400 

73,400 

73,400 

97,900 

97,900 

75 

320 

333 

451 

274 

330 

100 

50 

60 

70 

40 

60 

SOLID  INSULATIONS 


173 


Time  under  stress 

Potential 
applied 

Temperature  for  samples 

6 

7 

8 

9 

10 

Air 

Start 

100 
101 
102 
105 
111 
121 

100 
101 
102 
104 
108 
112 

101 
103 
104 
106 
108 
111 

103 
104 
105 
108 
111 
117 

100 
102 
103 
105 
107 
108 
115  pi 

100 
100 
100 
100 
100 
100 
mctured 

1  min  
2  min.           .  .    .  . 

16,000 
17,500 
19,000 
20,500 
22,000 
23,500 

3  min  
4  min  
5  niin 

5  min  5  sec 

5  min  46  sec..  .  . 
6  min  
6  min.  10  sec.  .  .  . 
6  min.  35  sec.  .  .  . 
7  min 

23,500 
23,500 
25,000 
25,000 

146  F 

unctui 
118 

ed  

114 

129 
135  pi 

nctured 

100 

mctured 

135 
140  p 

118  pu 

100 

7  min.  58  sec.  .  .  . 

26,500 

mncture 

d  

Endurance  Test 

Apply  40  Per  Cent,  of  1-minute  Period  Endurance  Voltage,  for  30-minute 
Periods  Endurance  Test,  with  10  Per  Cent.  Raise  in  Voltage  Each  Period 


Temp.,  deg. 


Resistance  in  megohms 


cent. 

11 

12 

13 

14 

15 

22 

74,300 

74,400 

74,400 

99,100 

49500 

75 

390 

420 

230 

290 

110 

100 

90 

70 

30 

60 

30 

Time  under  stress 

Potential 
applied 

Temperature 

11 

12 

13 

14 

15 

Air 

Start  

99 

103 

100 

107 

100 
133 
182  F 

101 
108 
uncture( 

99 
115 
I 

100 
100 

0.5  hr  

10,000 
11,000 
11,000 
11,000 
12,000 
13,000 
14,000 
14,000 
14,000 
15,000 
16,000 

34  min  

54  min  
1  hr  

198  pi 

mctured 
100 
100 
100 

104 
106 
106 

136 
143 
145  p 

108 
111 

118 

203  F 

112 
114 
122 
215  pi 
ed 

1.5  hr  

2hr  
2  hr.  23  min  
2  hr.  25  min  

unctui 

mctured 

2.5  hr  

3hr  
3  hr.  2  min  

imctur 

ed  .. 

174 


DIELECTRIC  PHENOMENA 


A  considerable  amount  of  data  is  given  here  for  the  1-minute 
time  test.  It  must  be  remembered  that  in  design  only  a  fraction 
of  the  maximum  gradient  corresponding  to  this  voltage  is  per- 
missible for  continuous  operation,  the  particular  per  cent,  depend- 
ing upon  the  design,  the  insulation,  the  rapidity  at  which  heat 
may  be  radiated,  or  conducted  away,  etc.  It  is  generally  10 
to  15  per  cent,  on  main  insulation;  it  is  often  as  low  as  5  per  cent., 
sometimes  as  high  as  30  per  cent. 

Strength  vs.  Thickness. — Insulation  tests  are  generally  made 
for  convenience  on  sheets  between  flat  terminals.  The  gradient 
at  the  edges,  even  when  these  are  rounded,  is  generally  higher 

than  the  average  gradient 
e/x.  This  edge  effect  is  differ- 
ent with  different  thicknesses 
of  insulation.  The  puncture 
voltage  per  centimeter  thick- 
ness is  always  greater  for  thin 
sheets  of  insulation  than  for 
thick  ones.  This  is  partly  due 
to  the  edge  effect  which  cannot 
be  corrected  for  and  becomes 
relatively  greater  as  the  thick- 
ness of  insulation  is  increased. 
(At  small  spacings  e/x  is  very 
nearly  the  true  gradient;  at 
large  spacings  .e/x  is  not  the 
true  maximum  gradient.) l  It 
is  also  greatly  due,  in  the  time 
tests,  to  the  better  heat  distri- 
bution and  dissipation  in  the 
thin  sheets  and  partly  due  to  the  fact  that  energy  is  necessary  for 
disruption,  so  that  when  the  rupturing  distance  is  limited,  as 
in  the  case  of  thin  sheets,  the  apparent  strength  increases.  Fig. 
154  shows  apparent  variation  in  strength  with  thickness.  Be- 
tween parallel  plates  the  apparent  strength  is  approximately: 


380 
360 

ntn 

\ 

\ 

\ 

OAA 

\ 

280 
260 
g.240 
«220 
S.200 

iiao 

^160 
§140 
120 
100 

\ 

\ 

\ 

x 

\ 

\ 

X 

\ 

^ 

| 

"""^""^ 

-- 

^_ 

80 
60 
40 
20 
n 

.02  .04 .06  .08.10.12 .14 .16.18.20.22.24.26.28 
Thickness- cm. 

FIG.  154. — Insulation  strength  vs. 
thickness. 


,.  -  ,(: 


vry 


where  g  and  a  are  constants  and  t  is  thickness. 

When  shielded  edges  are  used,  it  is  generally  best  to  make  in- 
sulation tests  under  oil  unless  it  is  desired  to  make  a  study  of  the 

1  Special  flat  terminals  are  sometimes  used  with  "shielded"  edges  so 
that  e/x  is  the  true  gradient. 


SOLID  INSULATIONS 


175 


effect  of  corona  on  the  insulation.  With  pointed  electrodes  the  in- 
stantaneous puncture  voltage  of  a  given  insulation  will  be  less  in 
oil  than  in  air.  This  is  not  because  the  oil  weakens  the  insulation 
but  because  corona  forms  on  the  point  in  air  and  spreads  over  the 
surface  giving  the  effect  of  a  flat  plate  electrode. 

Solid  and  Laminated  Insulation. — The  structure  of  most  insu- 
lations is  not  homogeneous.  If  a  given  insulation  is  tested  with 
terminals  of  varying  area  it  is  found  that  the  average  puncture 
voltage  becomes  lower  as  the  area  is  increased,  and  thus  the  chance 
of  it  covering  a  weak  spot  is  increased.  As  would  be  expected 
this  approximately  follows  the  probability  law  as  shown  in  Fig. 
155. 


5  20 

5 


\ 

PrJbabi 

ItyC 

urve 

\ 

/"N 

^ 

Exp 

erim 

enta 

Our 

76 

0123  45 

Radius  oi  JElat  Terminals-Gnu 


10 


18 


10 


15 


20 


12 


FIG.   155. — Insulation  strength  vs.  area      FIG.     156. — Variation    in    di- 
of  terminal.  electric    strength     at    different 

parts  of  a  piece  of  insulation. 

The  reason  that  the  experimental  curve  bends  down  is  that  the 
gradient  is  fairly  constant  until  the  terminal  becomes  small 
when  the  gradient  increases,  due  to  flux  concentration  with  the 
smaller  terminal.  If  the  curves  were  plotted  with  actual  gradients 
instead  of  voltages,  the  experimental  curve  would  follow  more 
closely  the  probability  curve.  The  experimental  gradient  curve 
would,  however,  for  the  smaller  sizes  bend  up  faster  than  the 
probability  curve,  due  to  greater  apparent  strength  for  smaller 
terminals,  as  for  small  spheres  in  the  case  of  air.  The  curve 
between  e/x  and  diameter  for  flat  terminals  of  the  larger  sizes 
when  the  concentration  at  the  edges  is  about  constant  should 
follow  the  probability  curve. 

For  example,  suppose  Fig.  156  represents  a  piece  of  solid  insula- 


176 


DIELECTRIC  PHENOMENA 


tion  0.025  mm.  thick  and  sufficiently  large  to  contain  every 
condition  of  "weak  spot."  Divide  this  into  six  equal  squares 
each  of  area  a.  The  strength  is  marked  on  the  various  areas. 
Assume  that  an  electrode  is  used  giving  no  edge  effect.  With 
electrode  of  area  a  six  tests  are  required  to  go  over  the  whole 
piece.  With  electrodes  of  area  2a  three  tests  are  required,  with 
area  3a  two  tests,  and  6a  one  test.  The  following  results  may  be 
obtained : 


Area 

No.  of 

Total  area 

Volts  per  mr 

i. 

electrode 

punctures 

covered 

Maximum 

Minimum 

Average 

a 

6 

6a 

20 

10 

14 

2a  

3 

6a 

18 

10 

13 

3a  

2 

6a 

12 

10 

11 

6a  

1 

6a 

10 

10 

10 

The  results  are  somewhat  similar  to  the  lower  points  of  the 
curve  in  Fig.  155. 

On  account  of  these  characteristics  alone  an  insulation  built 
up  of  laminations  is  much  better  than  a  solid  insulation  as  the 
weak  spots  in  the  laminations  are  not  likely  to  line  up.  It  is 
also  much  easier  to  make  better  and  more  uniform  insulation  in 
thin  sheets.  Another  probable  important  reason  for  greater 
strength  of  laminated  insulation  is  that  the  energy  distances  are 
interrupted  by  the  discontinuous  surfaces. 

Tests  are  useless  for  comparing  insulation  strengths  unless 
made  upon  some  standard  basis.  Great  caution  is  necessary 
in  the  use  of  tabulated  values  of  insulation  strength  in  design. 
On  account  of  the  variable  quality  of  solid  insulation,  tests  must 
be  continually  made  to  see  that  the  product  does  not  change. 
Vacuum  treatment  is  necessary  before  use  to  remove  moisture. 
Even  when  all  of  the  test  conditions  are  known,  experience  is 
necessary  to  judge  the  proper  factor  of  safety.  Aside  from  this, 
stress  concentrations  due  to  the  shapes  and  spacings  of  the  con- 
ductors must  always  be  considered  and  allowed  for.  It  is  gener- 
ally not  possible  to  do  this  with  mathematical  exactitude,  but 
approximation  must  be  made  with  all  factors  in  mind.  Care 
must  be  taken  that  the  solid  insulation  is  below  the  rupturing 
gradient  at  any  local  point.  If  such  a  point  is  broken  down 
locally  the  flux  becomes  still  further  concentrated.  The  puncture 


SOLID  INSULATIONS  177 

voltage  will  decrease  with  frequency,  even  over  the  commercial 
range,  due  to  increasing  loss  with  increasing  frequency. 
y  Impulse  Voltages  and  High  Frequency. — It  takes  energy  and 
therefore  time  to  rupture  insulation.  For  a  given  potential  a 
given  number  of  cycles  of  very  high  frequency  voltages,  where 
heating  does  not  result,  are  therefore  much  less  injurious  than 
the  same  number  of  cycles  at  low  frequency.  This  also  applies 
to  impulse  voltages  of  steep  wave  front.  Continuously  applied 
high  frequency  is,  however,  generally  very  injurious  for  two  dis- 
tinct reasons: 

(1)  On  account  of  the  very  great  loss  at  high  frequency  the 
insulation  may  be  literally  burned  up  in  a  very  short  time  even 
at  low  voltages.     This  condition  does  not  result  in  practice  from 
surges,  etc.,  on  low  frequency  lines,  but  in  high  frequency  genera- 
tors, and  transformers,  etc.     In  such  apparatus  it  is  important  to 
use  very  smooth  electrodes  to  prevent  local  concentration  of 
stress  and  charring  of  insulation.     This  is  especially  so  where 
contact  is  made  with  the  air.     If  a  local  brush  starts,  on  account 
of  the  great  loss,  it  becomes  very  hot  and  extends  out  a  consider- 
able distance. 

(2)  In  certain  apparatus  containing  inductance  and  capacity 
very  high  local  potential  differences  may  be  produced  by  reso- 
nance and  thus  cause  rupture  by  overpotential.     The  high  fre- 
quency thus  does  not  cause  the  rupture  directly  but  makes  it 
possible  by  causing  overpotential.     Local  concentration  of  stress 
may  also  result  in  non-homogeneous  insulation,  as  across  the 
condenser  and  resistance  combinations  in  Fig.  152. 

The  term  "high  frequency"  is  generally  used  in  such  a  way 
that  no  distinction  is  made  between  sinusoidal  high  frequency 
from  an  alternator,  undamped  oscillations,  damped  oscillations, 
impulses  of  steep  wave  front,  etc.  Naturally  the  effect  of  con- 
tinuously applied  undamped  oscillations  is  quite  different  from 
a  single  high-voltage  impulse  of  extremely  short  duration.  As 
the  effects  are  attributed  to  the  same  cause — "high  frequency" 
— apparent  discrepancies  must  result.  (See  comparative  tests, 
Table  LXXVI,  page  184.) 

If  the  time  of  application  is  limited  below  a  definite  value, 
higher  voltages  are  necessary  to  produce  the  same  results  in 
the  limited  time.  Impulse  voltages  of  steep  wave  front  many 
times  in  excess  of  the  rupturing  voltage  may  be  applied  to  insula- 
tions without  rupture  if  the  application  is  very  short — measured 


178  DIELECTRIC  PHENOMENA 

in  microseconds.  They  may  be  caused  in  practice  by  lightning, 
switching,  etc.  If  such  voltages  are  sufficiently  high,  complete 
rupture  may  result  at  once.  In  any  case  if  these  voltages  are 
higher  than  the  60-cycle  puncture  voltages  the  insulation  will 
be  damaged.  As  an  example,  an  impulse  voltage  equal  to  three 
times  the  60-cycle  puncture  voltage  may  be  applied  to  a  line 
insulator.  During  the  very  small  time  between  the  application 
of  the  voltage  and  the  arc-over  through  the  air,  the  insulator 
is  under  great  stress.  It  may  be  that  up  to  the  ninth  applica- 
tion of  such  a  voltage  there  is  no  evidence  of  any  injury,  while 
on  the  tenth  application  failure  results.  Each  stroke  has  con- 
tributed toward  puncture.  It  is  probable  that  each  application 
adds  to  or  extends  local  cracks.1 

Cumulative  Effect  of  Overvoltages  of  Steep  Wave  Front. — 
Voltages  greatly  in  excess  of  the  " rapidly  applied"  60-cycle 
puncture  voltage  may  be  applied  to  insulation  without  rupture 
if  the  time  of  application  is  sufficiently  short.  All  such  over- 
voltages  injure  the  insulation,  probably  by  mechanical  tearing, 
and  the  effect  is  cumulative.  A  sufficient  number  will  cause 
breakdown.  For  example:  A  piece  of  oiled  pressboard  3.2  mm. 
thick  has  a  rapidly  applied  breakdown  at  60  cycles  of  100  kv. 
maximum.  If  sinusoidal  impulses  reaching  their  maximum  in 
2.5  microseconds  are  applied,  the  number  of  impulses  to  cause 
break-down  is  as  follows: 

Kv.  maximum  of  Number   to   cause 

impulse  applied  breakdown 

100  00 

140  100 

150  16 

155  2 

165  1 

If  the  impulses  are  of  still  shorter  duration,  a  greater  number 
are  required  to  cause  breakdown  at  a  given  voltage.  Insulations, 
and  line  insulators,  are  often  injured  and  gradually  destroyed  in 
this  way  by  lightning. 

Strength  vs.  Time  of  Application. — It  was  stated  above  that 
the  strength  varies  with  the  time  of  application.  A  curve  is 
given  in  Fig.  153.  The  range  of  time  shown  in  this  curve  is  from 
a  few  seconds  ("instantaneous ")  to  an  indefinitely  long  time. 
Over  the  greater  part  of  the  plotted  curve  heating  is  a  factor  and 
the  great  decrease  is  principally  due  to  heating.  Where  the 

1  See  appendix. 


SOLID  INSULATIONS  179 

time  of  application  is  much  less  than  "  instantaneous "  value, 
and  heating  can  have  no  appreciable  effect,  the  strength  still 
increases  very  rapidly  as  the  time  of  application  is  decreased. 
The  increased  strength  at  this  part  of  the  curve  is  due  to  limited 
energy,  as  explained  on  page  177.  Some  values  from  an  actually 
measured  curve  are: 

(14  Layers  Impregnated  Paper  between  Concentric  Cylinders) 

R  =  0.67  cm. 
r  =  0.365  cm. 

Kilovolts  to  puncture 
Time,  sec.  (maximum) 

32.6 

60.0  37.5 

1.0  49.3 

0.1  61.0 

0.01  85.0 

0.001  113.0 

0.0001  196.0 

/    °-5  \ 
g  =  13.0(1  +  ^-^jkv./mm.  max. 

The  equation  of  the  strength-time  curve  over  the  complete 
range  obtained  from  an  examination  of  a  number  of  curves  is  of 
the  form 


_*\ 

Viy 


when  T  is  the  time  of  application  in  seconds,  and  gs  is  the 
gradient  in  kv./m.m.  for  indefinite  time.  The  equation  generally 
applies  well  over  a  range  from  infinite  time  to  0.01  seconds. 
For  shorter  periods  many  insulations  shatter  and  fail  at  voltages 
lower  than  the  equation  indicates. 

Both  a  and  gs  vary  with  the  thickness  of  the  insulation,  tem- 
perature, etc. 

In  order  that  the  strength  may  be  high  for  indefinite  time,  the 
loss  should  be  low. 

Permittivity  of  Insulating  Material. — In  design,  a  knowledge 
of  the  permittivity  of  insulating  materials  is  as  important  as  the 
dielectric  strength.  For  solid  insulations  the  permittivity  in- 
creases  with  the  specific  gravities  of  the  material  in  almost  a 
direct  ratio.  The  various  properties  of  some  of  the  common 
insulations  are  given  in  Table  LXXVI. 


180 


DIELECTRIC  PHENOMENA 


TABLE  LXXVI. — DIELECTRIC  STRENGTH  OF  SOLID  INSULATIONS 

Variation  of  Dielectric  Strength  with  Thickness  and  Number  of 

Layers.     (One-minute  Tests — 60-cycle — 10-cm.  Terminals  in  Oil.     Values 

Effective  Sine  Wave) 

PRESSBOARD 


No.  of 
layers 

Thickness  per 
layer,  mm. 

Total  thick- 
ness, mm. 

Kv./mm.  —  temperature  25  deg.  C. 

Varnished, 
kv./mm. 

Oiled  transil, 
kv./mm. 

Linseed  oil, 
kv./mm. 

1 

0.178 

0.178 

25.3 

25.3 

1 

0.254 

0.254 

26.3 

39.3 

23.6 

1 

0.508 

0.508 

21.0 

23.0 

1 

0.787 

0.787 

19.1 

33.5 

22.0 

1 

1.575 

1.575 

15.5 

29.2 

19.0 

1 

2.390 

2.390 

11.1 

23.0 

15.1 

1 

3.170 

3.170 

9.5 

21.1 

14.2 

2 

0.178 

0.356 

22.5 

21.0 

2 

0.254 

0.508 

17.7 

33.5 

19.7 

2 

0.508 

1.016 

12.8 

17.2 

2 

0.787 

1.574 

13.7 

22.9 

16.0 

2 

1.575 

3.150 

10.6 

19.7 

15.3 

2 

2.390 

4.790 

7.54 

16.1 

12.1 

2 

3.170 

6.340 

6.3 

14.7 

11.0 

4 

0.178 

0.712 

26.7 

16.6 

4 

0.254 

1.016 

22.6 

29.8 

15.3 

4 

0.508 

2.032 

16.8 

15.8 

4 

0.787 

3.148 

16.5 

20.6 

19.7 

4 

1.575 

6.300 

11.6 

13.65 

12.7 

4 

2.390 

9.560 

9.4 

11.5 

4 

*}  170 

12  680 

6.6 

TE 

o 

O  .  J-  1  \J 

0.178 

1.068 

25.5 

15.0 

6 

0.254 

1.524 

20.6 

27.5 

13.1 

6 

0.508 

3.048 

15.4 

14.4 

6 

0.787 

4.702 

14.9 

20.0 

17.8 

6 

1.575 

9.450 

11.3 

TREATED  WOOD 
Temperature  25  deg.  C. 


Across  grain 

kv./mm. 

With  grain 

kv./mm. 

1 

12 

6.42 

1 

30 

2.47 

1 

15 

4.53 

1 

60 

1.57 

1 

20 

3.85 

1 

90 

1.27 

1 

25 

3.02 

1 

120 

1.12 

SOLID  INSULATIONS 


181 


PAPER 

(Untreated) 


No.  of 
layers 

Thickness  per 
layer,  mm. 

Total  thickness, 
mm. 

25°  C.,  kv./mm. 

100°  C.,  kv./mm. 

1 

0.064 

0.064 

9.3 

9.3 

1 

0.127 

0.127 

8.7 

7.9 

1 

0.254 

0.254 

7.9 

7.3 

4 

0.064 

0.258 

8.7 

8.3 

4 

0.127 

0.508 

7.5 

6.7 

4 

0.254 

1.016 

6.6 

6.2 

8 

0.064 

0.516 

8.7 

8.1 

8 

0.127 

1.016 

7.4 

6.6 

3 

0.254 

2.032 

6.3 

6.0 

VARNISHED  CLOTH 


1 

0.305 

0.30 

26.2 

23.6 

2 

0.305 

0.61 

20.5 

19.7 

3 

0.305 

0.91 

18.5 

17.0 

4 

0.305 

1.22 

16.8 

14.9 

5 

0.305 

1.52 

15.5 

13.1 

6 

0.305 

1.83 

14.6 

11.5 

7 

0.305 

2.13 

14.0 

10.3 

8 

0.305 

2.44 

13.3 

9.2 

9 

0.305 

2.74 

'12.8 

8.3 

10 

0.305 

3.05 

12.3 

7.5 

HARD  RUBBER 


Thickness  per 

Total  thickness, 

Puncture 

voltage 

layer,  mm. 

mm. 

25°  C.,  kv./mm. 

100°  C.,  kv./mm. 

1 

0  0193 

59  7 

1 

0.0223 

55.6 

1 

0  0312 

48.7 

2  0 

2  0 

17  3 

3.0 
4.0 

3.0 
4.0 

14.2 
12.7 

5  0 

5  0 

11  8 

6.0 

6.0 

11.2 

12 


182 


DIELECTRIC  PHENOMENA 
MICA 


1 

0  0508 

0  0508 

96  5 

1 

0  1016 

0  1016 

88  7 

1 

0  1524 

0.1524 

75.5 

1 

0  2032 

0  2032 

62  6 

1 

0.5080 

0.5080 

26.1 



GLASS 


Total  thickness 

6.0 


Kv./mm. 

10 


The  kv./mm.  strength  of  glass  decreases  rapidly  with  increasing  thickness. 

PORCELAIN 


Total  thickness,  mm. 


Kv./mm. 


0.5 

1.0 

2.0 

5.0 

10.0 

15.0 


16.0 

14.5 

12.2 

11.0 

9.6 

9.2 


VARIATION  OF  INSULATION  STRENGTH  WITH  TIME  OF  APPLIED  VOLTAGE 


Material 

Thickness, 
mm. 

Time  to 
puncture,  min. 

25°  C. 
kv./mm. 

100°  C. 
kv./mm. 

Oil  impregnated  paper, 

1.90 

"Inst." 

39.4 

32.0 

30  layers,  60-cy.,   10- 

1 

33.1 

27.3 

cm.    diameter   discs, 

2 

31.0 

25.7 

round  edges. 

4 

29.2 

24.5 

6 

28.2 

23.6 

10 

26.8 

22.7 

20 

25.5 

21.6 

40 

23.6 

20.5 

60 

22.7 

19.7 

80 

22.1 

19.3 

100 

21.6 

19.0 

Note  that  for  a  given  thickness  the  strengths  of  materials  do  not  vary 
greatly  as  might  be  expected. 


SOLID  INSULATIONS 


183 


Material 


Thickness, 
mm. 


Time  to 

puncture, 

min. 


Puncture  voltage,  25°  C. 


1  layer, 
0.30  mm. 
kv./mm. 


5  layers, 
1.50  mm. 
kv./mm. 


10  layers, 
3.0  mm. 
kv./mm. 


Varnished  cloth,  0.30mm., 
60-cy.,  10-cm.  diameter 
in  air,  round  edges 


0.30 


"Inst.' 

0.1 

0.2 

0.5 

1.0 

2.0 

3.0 

5.0 

10.0 

20.0 


52.5 
37.7 
34.5 
32.8 
32.5 
32.1 
31.8 
31.5 
31.1 
30.2 


36.1 
27.5 
25.8 
22.9 
21.0 
20.3 
19.9 
19.8 
19.7 
19.6 


27, 
22 
19 
16 
14.3 
13.0 
12.6 
12.5 
12.3 
9.9 


PERMITTIVITY  OF  INSULATING  MATERIALS 


Permittivity 


Specific  gravity 


Asphalt 2-^ 

Bakelite 4-^ 

Cambric   (varnished) 4-^  to 

Fiber  (horn)  dry 2-# 

Fiber  (horn)  oil 4-^i  to  5 

Glass  (crown) 6 

Glass  (heavy  flint) 10 

Gutta  percha 3-^  to  4 

Lead  stearate 5.2 

Lead  palmitate 5.2 

Lead  oleate 5 

Mica 5  to  7 

Oil  (linseed) 

Oil  (transil) 2  to 

Paper  (dry) 2.6 

Paper  (paraffined)     3-^ 

Paper  (oiled) 4 

Paraffine 2  to  2.3 


1.15 

0.7  to  1 
0.9  to  1.5 

3  to  3. 5 
4.5 


0.95 
0.8to0.9 

1.00 

1.25 
0.9 


184  DIELECTRIC  PHENOMENA 

PERMITTIVITY  OF  INSULATING  MATERIALS. — Continued 


Permittivity 

Specific   gravity 

Pressboard    (dry)  

3 

1  25 

Pressboard  (oiled)  .    . 

4  to  6 

1  40 

Porcelain  

4~#  to  5 

2  4 

Rubber  (hard)  
Rubber  (vulcanized)  

Shellac 

3 
fc-H 

3 

Sulphur  

4 

Wood  (treated) 

3  to  3-y2 

0  8  to  0  9 

COMPARATIVE   INSULATION   STRENGTH   FOR   HIGH    FREQUENCY,    IMPULSE, 
OSCILLATION  AND  GO-CYCLE  VOLTAGES 

Temperature  30  deg.  C. 


60  Cycles 

High  frequency 
(alternator), 
90,000  cycles 

Damped    oscilla- 
tion, train  freq. 
120  sec.,  200,000 
cycles 

Single  impulse, 
sine  shape,  cor- 
responding to 
half  cycle  of 
200,000  cycle 

Thickness, 
mm. 

| 

Inst. 

1  min. 

Inst. 

1  min. 

Inst. 

1  min. 

kv./mm. 
(max.) 

kv./mm. 
(max.) 

kv./mm. 
(max.) 

kv./mm. 
(max.) 

Transil  Oil  between    Flat   Terminals — Square    Edge.     2.5-cm.    Diameter, 

0.25-cm.  Space 


17 

6.7 

30 

39 

Oiled  Pressboard.     10-cm.    Diameter — Square-edge    Discs   in   Oil 


35.5 
39  5 

31.0 
37  0 

9.5 
6  1 

7.3 
4  1 

37.0 
42  0 

29.0 
24  0 

72.0 

2.5 
5.0 

1 
2 

2  5 

1  76 

15  0 

3 

Varnished  Cambric 


53.0 

46  5 

19  5 

17  6 

108.0 

0.6 

2 

42.0 

31.0 

13.5 

10.0 

55.0 

56.0 

78.0 

1.5 

5 

37.0 

28.0 

10.0 

7.3 

49.0 

41.0 

70.0 

2.5 

8 

33.0 

27.5 

41.0 

30.5 

60.0 

3.6 

12 

SOLID  INSULATIONS 


185 


Energy  Loss  in  Solid  Insulation.— In  general,  energy  loss  in 

solid  insulation: 

(1)  Increases  with  increasing  voltage. 

(2)  Increases  with  increasing  temperature. 

(3)  Increases  with  increasing  frequency. 

(4)  Increases  with  increasing  moisture  content. 

(5)  Increases  with  increasing  impurities,  as  occluded  air,  etc. 


.30 
.28 
.26 
.24 

r::!s° 

g*    £ 

«.16g40 
H.12JJ30 

.08     20 
.06 

.04     10 
.02 
0 


4567 
Kilovolts  per  mm. 


FIG.  157. — Insulation  loss  and  power  factor  at  60  ~. 

(Oiled  pressboard  5 . 0  mm.  thick  between  parallel  plates  with  rounded  edges 
in  oil      Curves  1,  2,  3,  4,  watts  per  cu.  cm.     Curves  5,  6,  7,  8,  Power  factor.) 


'.20     20 
.18     18 


2.08g8.0 

g.06|6.0 

.04    4.0 

.02    2.0 

0       0 


20  30  40  50  60          70  80  90 

Temperature-Degrees  Cent. 


FIG.  158. — Insulation  loss  and  power  factor  vs.  temperature  at  60  ~. 
(Data,  Fig.  157.) 

For  good  uniform  insulation  free  from  foreign  material,  mois- 
ture, etc.,  the  loss  at  constant  temperature  and  frequency  varies 
approximately  as  the  square  of  the  applied  voltage.     The  author 
has  found  that  approximately  for  good  insulations 
p  =  afez  =  bfg*  X  10~6  watts/cu.  cm. 


186 


DIELECTRIC  PHENOMENA 


where/  =  frequency  in  cycles  per  sec. 
g  =  gradient  kv./mm.  effective. 

b  =  constant  varies  with  different  insulations.  It  is  8  to  10 
for  varnished  cambric  in  a  uniform  field,  and  thickness  in  order  of 
5  mm.  (25°  C.). 

Compare  calculated  values  with  values  given  in  Table  LXXVII 
at  both  60  cycles  and  high  frequency  (25  deg.  C.).  With  occluded 
air  or  water,  where  the  72r  loss  becomes  large  in  comparison  with 
the  "hysteresis"  loss,  the  rate  of  increase  is  greater.  Due  to 
combinations  of  resistance  and  capacity  it  may  then  take  the 
form,1  p  =  bfgz-{-  (c/2*/2  +  ag2) .  Fig.  157  shows  characteristic 
curves  between  energy  loss,  power  factor,  and  voltage  of  insula- 
tion in  good  condition. 

The  loss  increases  very  rapidly  with  temperature.  The  tem- 
perature curves  are  shown  in  Fig.  158.  The  effect  of  exposing 
to  the  air  is  also  shown.  Loss  in  different  insulations  is  given 
in  Table  LXXVII. 

TABLE  LXXVII. — INSULATION  LOSSES 
(Effective  Sine  Wave  60  Cycles) 


Total 
thickness, 
mm. 

Insulation 

No.  of 
layers 

Temp., 
deg.  C. 

Volts 
per  mm. 

Watts 
per 
cu.    cm. 

4.0 

Varnished  cloth 

15 

25 

4,000 

0.005 

' 

6,000 

0.015 

8,000 

0.035 

10,000 

0.060 

- 

12,000 

0.090 

4.0 

Varnished  cloth 

15 

90 

4,000 

0.025 

6,000 

0.075 

8,000 

0.150 

10,000 

0.240 

12,000 

0.350 

2.5 

Oil-treated  paper 

30 

25 

10,000 

0.040 

14,000 

0.070 

2.5 

Oil-treated  paper 

30 

60 

10,000 

0.043 

14,000 

0.080 

2.5 

Oil-treated  paper 

30 

90 

10,000 

0.050 

14,000 

0.100 

2.5 

Oil-  treated  paper 

30 

120 

10,000 

0.067 

14,000 

0.138 

These  losses  may  be  lower  or  very  much  higher,  depending  upon  the  con- 
dition of  the  insulation. 
1  See  Fig.  152, 


SOLID  INSULATIONS 


187 


HIGH  FREQUENCY  Loss  IN  DIFFERENT  INSULATIONS 
(Alexanderson,  Proc.  Inst.  Radio  Engrs.,  June,  1914) 


Volts  per 
mm. 

Effective 

Frequency 
kilocycle 

Material  (thickness  5  mm.) 

Glass 

Mica 

Varnished 
cambric 

Asbestos 

Loss 
watts, 
cu.  cm. 

P.  F. 
avg. 

Loss 
watts, 
cu.  cm. 

P.  F. 
avg. 

Loss 
watts, 
cu.  cm. 

P.  F. 
avg. 

Loss 
watts, 
cu.  cm. 

P.  F. 
avg. 

500 
500 

20 
40 

0.02 
0.05 

0   02 

0  7 

1.4 

0.04 

1:8 

0.08 

1.3 



500 

60 

0.08 



0.05 



0.12 

3.3 

2.0 

500 

80 

0.11 

0.08 

0.18 

32.0 

1000 

20 

0.08 



0.07 





3.0 

1000 
1000 
1000 

40 
60 
80 

0.20 
0.32 
0.40 

1.4 

0.12 
0.24 
0.35 

1.8 

0.28 
0.45 
0.65 

3.3 

5.3 

7.6 

32.0 



...... 

The  rate  of  increase  of  the  loss  with  the  frequency  will  vary 
greatly  if  the  insulation  contains  moisture.  If  the  moisture  is 
arranged  in  such  a  way  as  to  approximate  a  condenser  and  resist- 


Dielectric  Loss-Kw. 

«  H-  N>  CO  - 

1 

ll_ 

1 

I 

l\ 

j\ 
' 

/ 

—•• 

-^ 

L~ 

50                        100 

Kilovolts-High  Tension 

v 


0  10  20   o  30 

Temperature  Bise  above  21  C. 

FIG.  159.  —  Dielectric  loss  vs.  FIG.  160. — Dielectric  loss  vs.  tern- 
voltage  in  a  2750  kv-a,  120  kv,  60-  perature  in  a  3750  kv-a,  120  kv.  60~ 
transformer.  transformer  at  100  kv. 

ance  in  series,  as  in  Fig.  152,  the  loss  may,  over  a  limited  range, 
increase  approximately  as  the  square  of  the  frequency.  If  the 
insulation  is  in  good  condition  the  loss  may  increase  approxi- 
mately directly  as  the  frequency. 

The  best  method  of  comparing  different  insulations  is  by  meas- 
urement of  losses. 

Operating  Temperatures  of  Insulations. — The  maximum 
operating  temperature  of  insulations  is  indefinite.  For  low-vol- 


188 


DIELECTRIC  PHENOMENA 


tage  apparatus,  temperatures  not  high  enough  to  cause  direct 
electrical  failure  may  cause  mechanical  failure  in  short  periods 
by  drying  out  the  insulation,  cracking,  etc.  The  maximum  safe 
temperature,  at  which  the  life  is  not  greatly  shortened  mechan- 
ically by  cracking,  drying  out,  etc.,  varies  with  different  insula- 
tions, but  is  approximately  as  follows: 

Fibrous  materials,  cloth,  varnish,  etc 100  deg.  C. 

Asbestos,  mica  and  similar  materials,  in  combination  with  binders' 

varnish,  etc 150  deg.  C. 

Mica,  asbestos — alone very  high. 

These  values  are  given  without  consideration  of  the  electrical 
effects.  Often  the  electrical  properties  will  limit  the  tempera- 
tures below  these  values.  Heat  conductivity  must  be  considered 
in  design. 


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120 
110 

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a 

1234  56  78 

Total  Arcing  Distance.-.cm. 

FIG.  161. — Surface  arc-over  in  oil.     (Hendricks.) 


Surface  Leakage. — Strictly  speaking,  on  clean  dielectric  sur- 
faces, appreciable  leakage  does  not  occur.  What  is  generally 
termed  "  surf  ace  leakage"  is  a  rupture  of  one  dielectric  at  the 
surface  of  another  dielectric  by  overflux  concentration  due  to  differ- 
ence in  permittivities,  etc.  For  instance,  on  a  porcelain  insulator 
in  air  the  flux  may  be  sufficiently  concentrated  at  portions  of  the 
surface  to  cause  the  air  to  rupture.  The  appearance  is  that  of 
leakage  over  the  porcelain  surface.  "  Surf  ace  leakage"  then  is 
quite  indefinite,  and  for  a  given  leakage  distance  depends  upon 
the  position  and  shape  of  the  electrodes,  relative  capacities  of  the 
materials,  etc.  (See  Fig.  161.)  The  effects  of  actual  leakage  and 


SOLID  INSULATIONS  189 

apparent  leakage  in  air  may  be  seen  in  Table  LXXVIII,  page 
190.  In  (1)  the  spark-over  is  given  with  the  surface  out.  In 
(4)  the  decrease  must  be  due  to  actual  leakage  as  there  is  no 
flux  concentration.  In  (2)  and  (3)  flux  concentration  is  balanced 
against  increased  surface. 

Solid  Insulation  Barriers  in  Oil. — Properly  placed  barriers  of 
solid  insulation  in  oil  greatly  increase  the  strength  of  the  oil  spaces 
by  limiting  the  thickness  of  the  oil,  preventing  moisture  chains 
lining  up,  etc.  This  should  always  be  considered  in  design. 
In  placing  barriers,  however,  the  arrangement  should  be  such 
that  the  stress  on  the  oil  is  not  increased  by  the  higher  permit-  v 
tivity  of  the  solid  insulation.  Data  for  a  simple  arrangement  are 
given  in  Table  LXXVIII.  It  will  be  noted  that  in  most  cases  the 
strength  is  not  greatly  increased  on  account  of  difference  of  per- 
mittivity of  oil  and  solid  insulation.  The  reliability  is  much 
greater,  however. 

TABLE  LXXVIII. — PRESSBOARD  BARRIERS  IN  OIL 

Kv. 
Gap  0.24  cm.  effective 

Oil  only 23  .  0 

1 — 0.08-cm.  sheet  of  pressboard  midway  between  electrodes 24  .  7 

1 — 0.08-cm.  sheet  of  pressboard  against  one  electrode 22 .  7 

Kv. 

Gap  0.40  cm.  effective 

Oil  only 35.3 

2 — 0.08-cm.  sheets  of  pressboard  against  one  electrode 36.5 

Kv. 

Gap  0.56  cm.  effective 

Oil  only  53 . 9 

3 — 0.08-cm.  sheets  of  pressboard  against  one  electrode 44 .  0 

Kv. 

Gap  1.16  cm.  effective 

Oil  only ' '  96 . 0 

1 — 0.08-cm.  sheet  of  pressboard  0.1  cm.  from  each  terminal 95.3 

1 — 0.08-cm.  sheet  of  pressboard  0.33  cm.  from  each  terminal 102.0 

2 — 0.08-cm.  sheet  of  pressboard  at  midpoint 88 . 5 

1 — 0.08-cm.  sheet  of  pressboard  on  each  terminal 94.5 

Strength  of  pressboard — 0.08  cm.,  15  kv.;  0.16  cm.,  28  kv. 

Terminals  6  cm.  in  diameter,  rounded  with  a  3-cm.  radius  at  the  edges. 


190 


DIELECTRIC  PHENOMENA 
SURFACE  ARC-OVER  IN  AIR 


Effective 
kv.       kv./cm. 
(1)  7.6  cm.     Air     only     between     parallel 

plates.     Rounded  edges  128.0 


16.8 


•-5cm.-*} 


~  (2)  7.6  cm.  Over  corrugated  rubber  cylin- 
der  between  above  plates.  Surface 
oiled  94.0  12.4 

Surface  dry  87.0         11.4 


(3)  Corrugated    rubber    cylinder     between 

above  plates.     Surface  oiled  109 .0         14 . 3 

Surface  dry  89.0         11.7 


I 

7.6 
cm. 

1 

~»J3.8  cm.  U— 


(4)  Smooth  rubber  cylinder  between  above 

plates.    Oiled  surface  122.0         16.0 

Surface  dry  62.0  8.0 


NOTE. — Maximum  possible  kv.  arc-over  128.  Data  shows  that  although 
corrugations  increase  stress,  actual  gain  is  made  by  their  use  by  reduction 
of  true  leakage. 

Impregnation. — Insulations,  such  as  dry  paper,  with  low  dielec- 
tric strength  and  low  permittivity,  are  impregnated  with  oils  or 
compounds  of  high  strength  and  permittivity.  The  result  is  a 
dielectric  of  greater  strength  and  permittivity.  If  the  impreg- 
nating is  improperly  done,  for  instance  so  as  to  leave  oiled  spots 
and  unoiled  spots,  the  dielectric  strength  may  be  less  than  the 
dry  paper  alone.  This  is  due  to  the  difference  in  permittivities 
of  the  dry  and  oiled  spots,  which  causes  a  concentration  of  stress 
on  the  electrically  weak  dry  spots. 

Mechanical. — It  is  of  great  importance  to  arrange  designs  in 
such  a  way  that  local  cracking,  or  tearing  is  not  caused  by  high 
localized  mechanical  stresses.  This  is  especially  so  with  porce- 


SOLID  INSULATIONS  191 

lain,  as  in  the  line  insulators.  Expansion  of  a  metal  pin,  localized 
mechanical  stress  due  to  sharp  corners,  expansion  of  improper 
cement,  etc.,  will  cause  gradual  cracking  of  the  porcelain.  The 
so-called  deterioration  of  line  insulators  is  often  caused  in  this 
way. 

Direct  Current. — As  the  breakdown  depends  upon  the  maxi- 
mum point  of  the  voltage  wave,  the  direct-current  puncture  vol- 
tage in  air  and  oil  is  (\/2)  or  1.41  times  the  sine  wave  alternating 
puncture  voltage.  In  air  and  oil  there  is  very  little  loss  with 
alternating  current  until  the  puncture  voltage  i&  reached.  With 
solid  insulation  losses  occur  with  alternating  current  as  soon  as 
voltage  is  applied.  In  the  time  tests  the  insulation  is  thus 
considerably  weakened  by  heating,  especially  thick  insulation. 
This  causes  decreasing  breakdown  voltages  in  the  time  tests  as 
the  frequency  is  increased.  In  certain  insulations  the  loss  is 
very  small  for  direct  current.  The  gain  for  direct  current  in 
solid  insulation  in  the  time  tests  is  thus  greater  than  the  41% 
given  above.  See  appendix. 

Occluded  Air. — Where  careful  work  is  not  done  air  films  may 
be  occluded  in  solid  insulations.  Such  films  are  likely  to  break 
down  and  cause  local  heating,  chemical  action  and  finally, 
breakdown  of  the  solid  insulation.  When  such  films  are  un- 
avoidable, the  stress  should  be  limited  below  the  breakdown  of 
air.  The  strength  of  such  film  is  the  same  as  between  metal 
electrodes.  See  data  appendix. 


CHAPTER  VIII 
THE  ELECTRON  THEORY 

A  brief  review  of  the  electron  theory  will  be  given  in  this 
chapter. 

A  gas  is  a  very  poor  conductor  of  electricity.  A  condenser  or 
electroscope  may  be  left  charged  in  air  a  great  length  of  time  with- 
out considerable  loss  or  leakage.  If,  however,  the  surrounding 
air  and  the  terminals  of  the  condenser  or  electroscope  are  sub- 
jected to  the  action  of  X-rays,  ultraviolet  light,  or  radio-active 
substances,  the  leakage  becomes  quite  rapid.  All  of  these  agents 
in  some  way  act  as  carriers  or  change  the  nature  of  the  gas  so 
that  the  current  passes  from  terminal  to  terminal.  The  gas  is 
said  to  be  ionized. 


FIG.  162.— Cathode  ray  tube. 

If  terminals  are  placed  in  a  vacuum  tube  and  high  voltage  is 
applied  between  them,  a  visible  discharge  or  beam  of  rays  is  shot 
out  from  the  cathode.  These  cathode  rays  proceed  in  straight 
lines.  A  pin-hole  diaphragm  may  be  placed  in  their  path  and  a 
narrow  beam  obtained  (see  Fig.  162).  This  beam  may  be  de- 
flected by  a  magnetic  or  dielectric  field.  J.  J.  Thomson  pointed 
out  that  it  acts  in  every  way  as  if  it  were  made  up  of  negatively 
charged  particles  traveling  at  very  high  velocities.1  Every  test 
that  has  been  made  bears  this  out.  Where  the  particles  strike 
the  glass  it  becomes  luminescent.  These  particles  of  negative 
electricity  or  " charged"  corpuscles  are  called  electrons.  The 
velocity,  " charge,"  and  mass  of  these  electrons  have  been 
measured. 

1  These  rays  have  been  made  use  of  in  an  oscillograph.  In  this  instrument 
the  beam  acts  as  a  pointer  and  is  made  to  trace  a  curve  under  influence  of  the 
fields  produced  by  the  current  or  voltage  of  the  wave  which  is  being 
measured. 

192 


THE  ELECTRON  THEORY  193 

A  " charged"  body  in  motion  is  deflected  by  the  electric  fields 
in  the  same  way  as  a  wire-carrying  current.  The  deflection  de- 
pends upon  the  ratio  of  the  " charge"  e  and  the  mass  m.  By 
noting  the  deflection  of  the  cathode  rays  in  the  electric  field,  J.  J. 
Thomson  found  the  value  of  the  ratio  e/m.  The  most  accurate 
value  of  the  ratio  with  e  measured  in  electromagnetic  units  is 
1.8  X  107.  Each  ion  in  a  gas  acts  as  nuclei  in  the  condensation 
of  water  vapor.  The  condensation  in  the  presence  of  the  ions 
may  be  made  to  occur  by  change  of  pressure.  By  observing  the 
rate  of  fall  of  the  cloud  the  number  of  drops  or  electrons  can  be 
calculated.  If  the  total  " charge"  is  measured,  e  can  be  at  once 
obtained.  This  was  done  by  C.  T.  R.  Wilson,  e  was  also 
later  determined  by  Millikan  and  found  to  be  4.77  X  10-10 
electrostatic  units  or  1.6  X  10~20  electromagnetic  units.  The 
mass  of  the  electron  seems  to  be  about  1/1800  of  the  hydrogen 
atom,  or  the  same  mass  as  the  hydrogen  ion  in  electrolytic 
conduction.  This  mass  is  about  8.9  X  10-28  grams  when  the 
velocity  is  considerably  below  that  of  light,  and  apparently 
changes  with  velocity.  It  must  be  considered  as  that  determined 
by  force  divided  by  acceleration.  The  velocity  of  the  electron 
varies  from  107  to  109  cm./sec. 

The  beta  particle  of  radio-active  substances  is  identical  with  the 
cathode  particle  or  electron.  The  gamma  rays  are,  probably, 
ether  waves  produced  by  the  action  of  the  beta  particles  in  a 
way  similar  to  that  in  which  X-rays  are  produced  by  the  im- 
pingement of  cathode  particles  on  solids.  The  alpha  particle  is 
a  positively  charged  atom  of  helium. 

Elemental  positive  particles  corresponding  to  the  electron  have 
so  far  not  been  found.  Ion  is  a  general  term  used  for  positive 
or  negative  atoms  or  molecules,  electrons,  or  positive  particles. 

Take  two  electrodes  in  air  and  apply  some  low  potential 
between  them.  Direct  ultraviolet  light  upon  the  negative 
electrode.  If  the  voltage  is  gradually  increased,  the  current  in- 
creases almost  directly  up  to  (a),  Fig.  163.  There  is  then  a  con- 
siderable range  between  (a)  and  (b)  where  an  increase  in  voltage 
does  not  greatly  increase  the  current.  At  (6)  the  current  sud- 
denly increases  very  rapidly  with  increasing  voltage.  It  appears 
that  negative  " particles"  or  electrons  are  produced  or  set  free 
at  the  negative  conductor  by  the  ultraviolet  light.  These 
" particles  of  electricity"  are  attracted  to  the  positive  conductor 
and  thus  show  as  current  in  the  galvanometer  in  the  circuit. 
The  number  reaching  the  positive  conductor  increases  with  in- 


194 


DIELECTRIC  PHENOMENA 


creasing  voltage.  The  current  thus  increases  with  increasing 
voltage.  The  potential  at  (a)  is  sufficient  to  cause  practically 
all  of  the  negative  particles  that  are  produced  by  the  light  to 
reach  the  positive  conductor.  An  increase  of  the  voltage  above 
the  value  at  (a)  can  thus  cause  very  little  increase  in  current 
unless  a  new  source  of  ionization  is  applied  or  the  number  of 
ions  is  increased  in  some  way.  When  the  voltage  is  raised 
above  the  value  at  (6),  the  current  increases  very  rapidly  with 
increasing  voltage.  A  new  source  of  ionization  has  resulted. 

The  velocity  at  which  ions  travel  increases  with  increasing 
voltage  or  field  intensity.  The  new  source  of  ionization  results 
when  the  ions  have  reached  a  definite  velocity  in  their  mean  free 

path.  Townsend  has  ex- 
plained this  on  the  hypothesis 
that  ions  traveling  at  suffi- 
cient speed  generate  new  ions 
on  collision  with  neutral 
atoms  or  molecules.  Thus 
after  a  sufficient  voltage  is 
applied,  the  velocity  of  the 
ions  in  their  mean  free  path 
becomes  great  enough  to  pro- 
duce new  ions  by  collision  with 
atoms  or  molecules  by  separat- 
ing the  positive  and  negative 
parts  of  the  atoms  or  molecules.  These  in  turn  produce  new 
ions  so  the  ionic  density  increases  very  rapidly.  The  positive 
ions  travel  to  the  negative  conductor;  the  negative  ions  to  the 
positive  conductor.  It  seems,  however,  that  the  electron  plays 
the  principal  part  in  impact  ionization. 

It  may  be  of  interest  to  review  in  a  brief  way  how  the  law  of 
visual  corona  was  derived,  to  show  that  it  is  a  rational  law,  and 
to  illustrate  a  practical  application  of  the  electron  theory. 

In  1910  an  investigation  was  conducted  in  which  the  visual 
corona  voltages  of  various  sizes  of  polished  parallel  wires  at  various 
spacings  were  determined.1  For  any  given  conductor  the  voltage 
gradient  at  rupture,  gv,  was  found  to  be  constant  independent  of 
the  spacing  (except  at  very  small  spacings),  but  increased  very 
rapidly  as  the  radius  of  the  conductor  was  decreased.  Thus  air 
apparently  had  a  greater  strength  for  small  conductors  than  large 
1  F.  W.  Peek,  Jr.,  Law  of  Corona,  A.I.E.E.,  June,  1911. 


X 

E 

2 

\ 

a 

a 

Sa 

urn 

ion 

b 

y 

y 

/ 

Volts 


'  FIG.  163. — Variation  of  current  with 
voltage  through  ionized  space  between 
parallel  plate  electrodes. 


THE  ELECTRON  THEORY  195 

ones.  This  was  formerly  pointed  out  by  Prof.  Ryan.  The  curve 
of  experimental  data  between  gv  and  radius  r  was  found  to  be 
regular  and  continuous.  A  number  of  equations  could  readily  be 
written  which  would  fit  these  data.  It  was  desired,  however,  to 
establish  or  build  up  a  rational  equation.  The  old  idea  of  air  films 
at  the  surface  of  the  conductors  was  abandoned  after  tests  with 
very  light  (aluminum)  and  very  heavy  (tungsten)  metals  showed 
that  the  density  of  the  metal  of  the  conductor  had  no  influence 
on  gv,  which  should  be  the  case  if  the  difference  were  caused  by 
air  films,  as  the  air  film  should  vary  with  the  density  of  the 
conductor. 

A  rational  law  of  visual  corona  was  deduced  from  the  data, 
as  follows: 

Energy  of  some  form,  be  this  the  ^.  -^-  of   the  energy   of 

the  moving  ions,  or  whatever  form  it  may,  is  necessary  to  rupture 
insulation.  This  is  borne  out  by  experiments  with  transients, 
which  show  that  finite  time  is  necessary  to  rupture  insulation; 
that  if  this  time  be  limited  the  voltage  must  be  increased  to 
accomplish  the  same  results  in  the  limited  time,  also  heating 
results  at  rupture,  etc.  These  imply  definite  finite  energy. 

The  gradient  or  stress  to  rupture  air  in  bulk  in  a  uniform  field, 
0o,  should  be  constant  for  a  given  air  density  or  molecular  spacing. 
In  a  non-uniform  field,  as  that  around  a  wire,  the  breakdown 
strength  of  air,  g0,  is  first  reached  at  the  conductor  surface;  at  an 
infinitely  small  distance  from  the  conductor  surface  the  stress 
is  still  below  the  rupturing  gradient.  Hence,  in  order  to  store  the 
necessary  finite  rupturing  energy  the  gradient  at  the  conductor 
surface  must  be  increased  to  gv,  so  that  at  a  finite  distance 
away  the  gradient  is  g0.  This  means  that  a  finite  thickness  of 
the  insulation  must  be  under  a  stress  of  at  least  g0.  The  ruptur- 
ing energy  is  in  the  zone  between  gv  and  g0.  The  thickness  of 
the  zone  should  be  a  function  of  the  conductor  radius.  It  was 
found  that  at 

cm. 


from  the  conductor  surface  the  gradient  at  rupture  is  always  con- 
stant and  30  kv./cm.  (at  standard  air  density).  The  relation 
between  gv  and  r  may  now  be  directly  expressed  by  the  simple 
law 

kv'/cm- 


196  DIELECTRIC  PHENOMENA 

For  parallel  planes  or  for  air  in  bulk 


r  = 


Thus  the  strength  of  air  is  constant  and  equal  to  30  kv./cm., 
but  in  non-uniform  fields  is  apparently  stronger,  as  explained 
above.  If  the  air  is  made  less  dense,  that  is  the  molecular  spac- 
ing is  changed,  the  strength  of  air  in  a  uniform  field  should  de- 
crease directly  with  the  air  density. 


However,  for  non-uniform  fields,  the  energy  distance  should  also 
change  thus 


The  complete  equation  including  air  density  factor  was  found 
to  take  the  simple  rational  form 


This  equation  holds  for  values  of  5  as  low  as  0.02  for  corona  on 
wires.     For  a  given  pair  of  electrodes  the  strength,  g,  decreases 

with  decreasing  d  until  a 
minimum  value  is  reached. 
g  then  increases  very  rapidly 
with  decreasing  5.  See  Fig. 
164.  The  value  of  5  at  which 
the  minimum  g  occurs  in  a 
uniform  field,  as  between 
spheres  at  small  spacings,  x, 
depends  upon  the  product 

FIG.  164.— Variation  of  strength  of  of  x  and  pressure,  p,  or  of  a; 
air  with  density  showing    increase   in          -,    .       ,-,,  •  ,,         ,, 

strength  at  very  low  densities.  and  5-     This  means  that  the 

spark    potential    is    constant 

as  long  as  the  product  of  the  pressure  or  density  and  spark  length 
remain  constant.     Thus  where 


or 


px  —  k 
dx  =  kl 


the  spark-over  voltage  is  constant  independent  of  the  individual 
values  of  p  and  x.  See  appendix.  This  is  known  as  Paschen's 
Law.  At  very  high  vacuum  the  separation  of  the  molecules 


THE  ELECTRON  THEORY  197 

may  be  of  a  fairly  high  order  compared  to  the  dimension  of  the 
tube.  There  is,  thus,  very  little  ionization  by  collision,  and  the 
apparent  strength  becomes  high.  At  still  higher  vacuum,  as 
used  in  the  best  X-ray  tubes,  the  only  source  of  ionization  is 
from  the  conductors  themselves.  In  the  latest  tubes  the  cathode 
is  hot  and  is  the  only  source  of  ions.  The  number  can  be  con- 
trolled by  the  temperature  of  the  cathode.1 

If  the  energy  distance  is  limited  to  less  than 0.301\/r,  by  placing 
the  conductors  close  together,  the  apparent  gradient  should  in- 
crease. This  also  is  borne  out  by  experiment.  The  visual  tests 
on  various  forms  of  electrodes,  as  spheres,  wires,  planes,  etc.,  as 
well  as  loss  measurements,  all  point  to  an  energy  storage  distance 
and  a  constant  strength  of  air  of  30  kv./cm. 

For  continuously  applied  high  frequency  where  the  rate  of  energy 
or  power  is  great,  frequency  may  enter  into  the  energy  thus, 


0.301-J^  0  (/) 

and  spark-over  take  place  at  somewhat  lower  voltages.  Where 
the  time  is  limited,  as  by  an  impulse  of  steep  wave  front,  a  much 
higher  voltage  should  be  required  to  start  arc-over.  This  is 
also  borne  out  by  experiment. 

Thus  far  the  form  of  this  rupturing  energy  has  not  been  con- 
sidered as  it  was  unnecessary,  in  order  to  develop  a  rational 
working  equation. 

When  low  potential  is  applied  between  two  conductors  any 
free  ions  are  set  in  motion.  As  the  potential  and,  therefore, 
the  field  intensity  or  gradient  is  increased,  the  velocity  of  the 
ions  increases.2  At  the  gradient  of  g0  =  30  kv./cm.  (5  =  1) 
the  velocity  of  the  ions  becomes  sufficiently  great  over  the  mean 
free  path  to  form  other  ions  by  collision.  This  gradient  is 
constant  and  is  called  the  dielectric  strength  of  air.  When  ionic 
saturation  is  reached  at  any  point,  the  air  becomes  conducting 
and  glows,  or  there  is  corona  or  spark. 

Applying  this  to  parallel  wires:  when  a  gradient  gv  is  reached 
at  the  wire  surface,  any  free  ions  are  accelerated  and  produce 
other  ions  by  collision  with  molecules,  which  are  in  turn  acceler- 
ated. The  ionic  density  is  thus  gradually  increased  by  successive 
collision  until  at  0.301  Vr  cm.  from  the  wire  surface,  where  g0  = 
30,  ionic  saturation  is  reached,  or  corona  starts.  The  distance 

1  Coolidge  X-ray  tube. 

2  See  also  explanation  given  in  Theory  of  Corona,  Bergen  Davis,  A.I.E.E., 
April,  1914. 


198  DIELECTRIC  PHENOMENA 

0.301  \/r  cm.  is,  of  course,  many  times  greater  than  the  mean 
free  path  of  the  ion,  and  many  collisions  must  take  place  in  this 
distance.  Thus,  for  the  wire,  corona  cannot  form  when  the 
gradient  of  g0  is  reached  at  the  surface,  as  at  any  distance  from 
the  surface  the  gradient  is  less  than  g0. 

The  gradient  at  the  surface  must  therefore  be  increased  to  gv 
so  that  the  gradient  a  finite  distance  away  from  the  surface 
(0.301  Vr  cm.)  is  g0.  That  is  to  say,  energy  is  necessary  to  start 
corona,  as  noted  above.  g0  the  strength  of  air,  should  vary  with 
5;  gvy  however,  cannot  vary  directly  with  d,  because,  with  the 
greater  mean  free  path  of  the  ion  at  lower  air  densities,  a  greater 
"accelerating"  or  energy  distance  is  necessary.  In  the  equation, 
a  =  O.SOlVr/d;  that  is,  a  increases  with  decreasing  5. 

When  the  conductors  are  placed  so  close  together  that  the  free 
•accelerating  or  energy  storage  distance  is  interfered  with,  the 
gradient  gv  must  be  increased  in  order  that  ionic  saturation  may 
be  reached  in  this  limited  distance. 

Over  a  wide  range,  initial  ionization  of  the  air  cannot  affect 
the  starting  voltage  of  a  steadily  applied  low-frequency  e.m.f. 
since  such  ionization  must  necessarily  be  very  small  compared 
to  the  residual  ionization  after  each  cycle.  If  the  ionization  is 
very  small  when  such  a  voltage  is  first  applied  an  appreciable 
time  is  necessary  before  corona  starts,  but  the  starting  voltage 
is  not  affected. 

The  initial  ionization  should,  however,  have  a  considerable 
effect  upon  transient  voltages  of  short  duration,  steep  wave-front 
voltages,  etc.  Thus,  if  for  given  electrodes,  the  time  of  applica- 
tion is  less  than  that  normally  necessary  to  bring  the  initial  ioniza- 
tion up  to  ionic  saturation,  a  higher  voltage  should  be  required 
to  cause  corona  or  spark-over  in  the  limited  time.  Experiments 
show,  however,  that  even  with  impulse  voltages  the  initial  ioniza- 
tion may  be  varied  over  a  great  range  without  appreciable  change 
in  the  impulse  spark-over  voltage  of  a  given  pair  of  electrodes  in 
open  air.  The  effect  of  initial  ionization  may  be  observed  to  a 
greater  extent  at  low  air  densities,  where  the  number  of  free  ions 
may  be  made  an  appreciable  per  cent,  of  ionic  saturation.  When 
the  electrodes  are  of  such  a  nature  as  to  require  considerable  brush 
discharge  in  the  path  of  the  spark  before  spark-over,  the  steep 
wave-front  voltage  required  to  cause  discharge  over  a  given  gap 
is  much  higher  than  the  required  steady  voltage.  If  spheres 
and  needles,  set  to  spark-over  at  the  same  60-cycle  voltage,  are 
placed  in  parallel  and  impulse  voltage  of  steep  wave  front  ap- 
plied, spark-over  will  take  place  across  the  spheres  only. 


CHAPTER  IX 
PRACTICAL  CORONA  CALCULATIONS  FOR  TRANSMISSION  LINES 

Summary  of  Various  Factors  Affecting  Corona. — If  potential  is 
applied  between  the  conductors  of  a  transmission  line  and  gradu- 
ally increased,  a  point  is  reached  when  wattmeters  placed  in  the 
circuit  begin  to  read.  The  watt  loss  is  low  at  first  but  increases 
with  increasing  voltages.  At  the  point  where  the  meters  begin 
to  read,  a  hissing  noise  is  heard,  and  if  it  is  quite  dark,  localized 


16 

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Effective  Kilo-Volts   BetweeiLLiiies 

FIG.  166. — Characteristic    corona  loss, 
current,   and  power  factor  curves. 
(Line  A.     Conductor  length,  109,500 

cm.  (total).    Spacing, 310 cm.   Diameter, 

1.18   cm.   (3/0  cable).    Temp.,  12°   C. 

Bar.,  75.) 


Effective  Kilo-Volts    Between  Lines 

FIG.  167. — Loss  near  the  critical 
voltage  of  new  and  old  cables. 
(Data  Fig.  166.  Line  calcu- 
lated, x,  new  cable:  o,  weathered 
cable). 


streamers  and  glow  points  can  be  noticed  at  spots  on  the  con- 
ductors. These  first  streamers  are  caused  by  dirt  and  irregulari- 
ties. The  watt  increase  is  still  gradual.  Slowly  raising  the 
voltage,  the  true  visual  critical  corona  point  is  finally  reached. 
The  effect  is  striking;  corona  suddenly  jumps  out,  as  it  were,  all 
along  the  line.  The  line  immediately  becomes  very  noisy,  and 
the  loss  increases  very  rapidly  with  increasing  voltage.  The 
intensity  of  the  light  also  increases  with  increasing  voltage.  If 

199 


200  DIELECTRIC  PHENOMENA 

one  is  close  to  the  conductors  an  odor  of  ozone  and  nitrous  oxide, 
the  result  of  chemical  action  on  the  air,  is  noticed.  There  is, 
thus,  heat,  chemical  action,  light,  and  sound  in  the  process  of 
corona  formation.  These  naturally  all  mean  energy  loss. 

It  becomes  of  great  importance  in  the  design  of  high- voltage 
transmission  lines  to  know  the  various  factors  which  affect  the 
corona  formation,  and  to  have  simple  working  formulae  for  pre- 
determining the  corona  characteristics,  so  that  the  corona  loss 
will  not  be  excessive. 

Loss  begins  at  some  critical  voltage,  which  depends  upon  the 
size  and  spacing  of  the  line  conductors,  altitudes,  etc.,  and  in- 
creases very  rapidly  above  this  voltage.  Figs.  166  and  167  show 
typical  corona  loss  curves  during  fair  weather. 

An  extensive  investigation  on  an  experimental  transmission 
line  (see  Fig.  168)  has  shown  that  the  corona  loss  in  fair  weather 
is  expressed  by  the  equation: 

p  =  a(f  +  c)(e  -  eoy 

where   p  =  loss  in  kilowatts  per  kilometer  length  of  single-line 

conductor. 

e    =  effective  value  of  the  voltage  between  the  line  con- 
ductors and  neutral  in  kilo  volts.1 
/    =  frequency, 
c   =  a  constant  =  25 
and  a  is  given  by  the  equation 

a  =  -d 

where  r    =  radius  of  conductor  in  centimeters. 

s    =  the  distance  between  conductor   and  return   con- 
ductor in  centimeters. 
5  =  density  of  the  air,  referred  to  the  density  at  25 

deg.  C.  and  76  cm.  barometer  as  unity. 
A  =  a  constant  =  241. 

e0  =  the  effective  disruptive  critical  voltage  to  neutral,  and 
is  given  by  the  equation 

e0  =  m0g0br  loge  s/r  kv.  to  neutral1 

where  g0  is  the  disruptive  gradient  of -air  in  kilovolts  per  centi- 
meter at  25  deg.  C.  and  76  cm.  barometer,  and  is  constant  for  all 

1  Hence,  in  single-phase  circuits,  e  is  one-half  the  voltage  between  con- 
ductors. In  three-phase  circuits,  e  is  1/V3  times  the  voltage  between 
conductors. 


FIG.  165. — Corona  at  230  kv.   Line  A.    3/0  cable.    310cm.  (122  in.)  spacing. 

(Facing  page  200.) 


FIG.  168. — Experimental  transmission  line. 


CORONA  CALCULATIONS  FOR  TRANSMISSION  LINES  201 

practical  transmission  line  sizes  of  conductor  frequencies,  etc. 
For  very  small  conductors  Qd  is  used.     (See  pages  136,  141,  142.) 

g0    =  21.1  kv.  per  cm.  (effective). 

m0       is  a  constant  depending  upon  the  surface  condition  of 
the  conductions,  and  is 

m0  =  1  for  perfectly  smooth  polished  wire, 

m0  =  0.98  to  0.93  for  roughened  or  weathered  wires,  and 
decreases  to 

m0  =  0.87  to  0.83  for  seven-strand  cables  (where  the  radius 

is  taken  as  the  outer  radius  of  the  cable)  . 

Luminosity  of  the  air  surrounding  the  line  conductors  does  not 
begin  at  the  disruptive  critical  voltage  e0,  but  at  a  higher  voltage  ev, 
the  visual  critical  voltage.  The  visual  critical  voltage,  ev,  is  much 
higher  for  small  conductors  than  the  disruptive  critical  voltage,  e0; 
it  is  also  higher  for  large  conductors,  but  to  a  less  extent.  For 
very  small  conductors  ed  replaces  e0.  (See  page  141.) 

While  theoretically  no  appreciable  loss  of  power  should  occur 
below  the  visual  voltage,  ev,  some  loss  does  occur,  due  to  irregu- 
larities of  the  wire  surface,  dirt,  etc.,  as  indicated  by  brush  dis- 
charges, and  local  corona  streamers.  (See  page  143.) 

As  the  loss  between  ev  and  e0  depends  upon  dirt,  roughened 
condition  of  the  wire  surface,  etc.,  it  is  unstable  and  variable  and 
changes  as  the  surface  of  the  conductors  changes.  For  the  larger 
sizes  of  stranded  transmission  conductors  in  practice  the  surface 
is  generally  such  that  the  loss  approximately  follows  the  quadratic 
law,  even  between  e0  and  ev.  This  is  shown  by  the  circles  in 
Fig.  167,  which  are  measured  points  on  a  weathered  conductor. 
The  crosses  indicate  how  the  points  come  on  a  new  conductor. 
For  a  small  conductor  the  difference  between  the  calculated  and 
measured  losses  on  the  section  of  the  curve  between  e0  and  ev 
is  still  greater.  Above  ev  the  curves  coincide  and  follow  the 
quadratic  law.  In  practice  it  is  rarely  admissible  to  operate 
above  the  e0  voltage.1  Cases  are  known  in  which  conductors 
have  deteriorated  by  the  action  of  nitric  acid  formed  by  exces- 
sive brush  discharge. 

It  is  interesting  to  note  that  the  loss  below  ev  actually  follows  the 
probability  curve 


but  this  need  not  be  considered  in  practice. 

1  Operation  at  e0  voltage  at  high  altitudes  gives  relatively  greater  margin 
and  less  loss  than  at  sea  level  as  there  is  greater  difference  between  ev  and  e0. 


202 


DIELECTRIC  PHENOMENA 


The  corona  loss  is: 

(a)  A  loss  proportional  to  the  frequency  /  plus  a  small  constant 
loss.  . 

(6)  Proportional  to  the  square  of  the  excess  voltage  above  the 
disruptive  critical  voltage,  e0. 

(c)  Proportional  to  the  conductor  radius  r  and  log  s/r.  The 
critical  voltage  thus  increases  very  rapidly  with  increasing  r, 
and  to  a  less  extent  with  spacing. 

The  disruptive  critical  voltage,  e0,  is  the  voltage  at  which  the 
disruptive  voltage  gradient  of  the  air  is  reached  at  the  conductor 
surface.  Hence  it  is: 

(a)  Proportional  to  the  conductor  radius  r  and  loge  s/r.     The 

critical  voltage  thus  increases 
very  rapidly  with  increasing  r, 
and  to  a  much  less  extent  with 
increasing  s. 

(6)  Proportional  to  the  air 
density  or  becomes  very  low  at 
high  altitudes. 

(c)  Dependent  somewhat  on 
the  conditions  of  the  conductor 
surface,  as  represented  by  m. 

The  effects  of  various  atmos- 
pheric conditions  and  storms  on 
the  critical  voltage  and  loss  will 
now  be  considered. 

(a)  Humidity  has  no  effect  on 


3  io 


»-«     »H     r*     rt    i-H     .-I     ft     r-trHr-4 

Kilo-Volts  Effective 


FIG.  169. — Comparison  of  fair 
weather  and  storm  loss. 


53  the  critical  voltage. 

(6)  Smoke  lowers  the  critical 
voltage  and  increases  the  loss. 

(c)  Heavy  winds  have  no  effect 
on  the  loss  or  critical  voltage  at  ordinary  commercial  frequencies. 

(d)  Fog  lowers  the  critical  voltage  and  increases  the  loss. 

(e)  Sleet  on  the  wires,  or  falling  sleet,  lowers  the  critical  voltage 
and  increases  the  loss.     High  voltages  do  not  eliminate  sleet 
formation. 

(/)  Rain  storms  lower  the  critical  voltage  and  increase  the  loss. 

(g)  Snow  storms  lower  the  critical  voltage  and  increase  the  loss. 

(h)  At  high  altitudes  the  loss  is  very  much  greater  on  a  given 
conductor,  at  a  given  voltage,  than  it  is  at  sea  level.  For  a  given 
voltage  larger  conductors  must  be  used  at  high  altitudes. 


CORONA  CALCULATIONS  FOR  TRANSMISSION  LINES  203 

Fig.  169  shows  a  typical  loss  curve  during  storm  and  a  corre- 
sponding fair  weather  curve. 

Practical  Corona  Formulae  and  Their  Application.  —  The  for- 
mulae required  for  the  determination  of  the  corona  characteristics 
of  transmission  lines  are: 

METRIC  UNITS 

Disruptive  Critical  Voltage 

e0  =  21.1m0  r  5  loge  s/r  kv.  to  neutral  (35) 

Power  Loss 

-  ~  -        krkm-  of  single 


Where  the  conductors  are  small   use  formulas   (34a),    (35a), 
and  (36),  Chapter  V. 

Visual  Critical  Voltage 

ev  =  2l.lmv8r(l  +  -^7=-)  loge  s/r  kv.  to  neutral          (20) 

/ 

3.926 


273  +  t 
where 

e  =  effective  kilo  volts  to  neutral  applied  to  the  line1 

5  =  air  density  factor 

=  1  at  25  deg.  C.,  76  cm.  barometer 

6  =  barometric  pressure  in  centimeters 
t    =  temperature  in  degrees  Centigrade 
T    =  radius  of  conductor,  centimeters 

s    =  spacing  between  conductor  centers  in  centimeters 
/    =  frequency  cycles  per  second. 

For  approximating  storm  loss  consider  e0  =  0.8  of  fair  weather 
value  in  formula  (35). 
Irregularity  Factors 

m0  =  1  for  polished  wires 

=  0.98  —  0.93  for  roughened  or  weathered  wires 
=  0.87  —  0.83  for  seven-strand  cables 
mv  =  m0  for  polished  wire    =  1 
mv  '=  0.72  for  local  corona  all  along  cable 
mv  =  0.82  for  decided  corona  all  along  cable. 

1  e   =  volts  between  line  times  l/\/3  for  three-phase  lines  and  volts 
between  line  times  ^  for  single-phase  or  two-phase  lines. 


204 


DIELECTRIC  PHENOMENA 


ENGLISH  UNITS 
Disruptive  Critical  Voltage 

e0  =  I23m0rd  logic  s/r  kv.  to  neutral 
Power  Loss 


(350 


,21n_5  kw.  of  single  conductor  m/, 
-  eo)210  5 


390 
P  =   -- 


Where  the  conductors  are  small  use  f  ormulse  (34a)  ,  (35a)  and 
36,  Chapter  V. 

Visual  Critical  Voltage 

ev  =  123mvdr(l  +    '  ._  )  logic  s/r  kv.  to  n'eutral      (200 
V  V  dr  / 

17.96 


where 


459  +  t 

e  =  effective  kilovolts  to  neutral  applied  to  the  line1 

5  —  air  density  factor 

=  1  at  77  deg.  F.  and  29.9  in.  barometer 

6  =  barometric  pressure  in  inches 

t  =  temperature  in  degrees  Fahrenheit 

r  =  radius  of  conductor,  inches 

s  =  distance  between  conductor  centers  in  inches 

/  =  frequency,  cycles  per  second. 


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Values  of  S/r  Values  of  s/r 


FIG.  170. 


FIG.  171. 


le  =  volts  between  line  times   l/\/3  for  three-phase  lines  and  volts 
between  line  times  M  for  single-phase  or  two-phase  lines. 


CORONA  CALCULATIONS  FOR  TRANSMISSION  LINES  205 


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1000         2000          3000         4000 

Altitn-d.e-Met.ers 


FIG.  172. — Approximate  barometric  readings  at  different  altitudes. 

In  order  to  illustrate  the  use  of  the  formulae,  the  following 
practical  example  is  taken: 


Given:  three-phase  line 
Length 
Spacing 
Conductor 
Max.  temperature 
Elevation 
Barometer  (from  Fig.  172)  28.85  in. 

120 

s/r  = 


EXAMPLE 

60  cycles 
100  miles 
120  in. 

1/0  cable — diam.  0.374  in. 
100  deg.  F. 
1000  ft. 


Then 


0.187  ' 
logio  s/r  =  2.81  (from  Fig.  171  or  tables) 

Vr/s  =  0.0394  (from  Fig.  170  or  calculated) 
17.96          17.9  X  28.85 


d   = 


=  0.925 


459  +  2.         459+100 
m0  =  0.87 

e0  =  123m0r5  logw  s/r  =  123  X  0.87  X  0.187  X  0.925  X  2.81  (35') 
=  52.0  kv.  to  neutral 

390 
P  =  -y-  (/  +  25) Vr/s(e  -  e0)210~5  (34') 

=  0.014(e  —  52. 0)2  kw.  per  mile  of  single  conductor. 
Since  there  are  three  conductors: 

p  =  0.042(e  —  52. 0)2  kw.  per  mile  of  three-phase  line. 
The  conductor  (100  deg.  F.,  1000  ft.  elevation)  would  glow  at 

ev  =  123mvdr  (  1  +  -^=1  logio  s/r  =  62.6  kv.  to  neutral  (200 
\  v  5r/ 


206 


DIELECTRIC  PHENOMENA 


or  62.6  X  1.73  =  108.3  kv.  between  lines. 

More  decidedly  at 

71.3  X  1.73  =  123.4  kv.  between  lines. 

The  visual  corona  cannot  be  observed  except  on  a  very  dark 
cloudy  night. 

To  show  the  effect  of  altitude,  the  characteristics  of  the  same 
line  are  calculated  for  10,000  ft.  elevation  and  tabulated  in  Table 
LXXIX.  At  this  altitude 

p   =  0.0599(e  -  36.8)2  kw.  per  mile  of  three-phase  line 
e0  =  36.8  kv.  to  neutral. 

(mv  =  0.72)  81.5  kv.  local. 
Visual  corona  between  lines  * 

(mv  =  0.82)  92.7  kv.  decided. 
TABLE  LXXIX. — CORONA   Loss    AT    DIFFERENT    OPERATING   VOLTAGES 


Kw.  per  mile  and  total  in  100  miles 

1000  ft.  elevation 

10,000  ft.  elevation 

Kv.  bet. 

Kv.  to 

lines 

neutral   e 

Fair  weather 

Storms 

Fair  weather 

Storms 

p  per 

p  per 

p  per 

p  per 

mile, 

100  miles 

mile, 

100  miles 

mile, 

100  miles 

mile, 

100  miles 

3  cond. 

3  cond. 

3   cond. 

3  cond. 

50 

28   9 

60 

34.7 

1.7 

170 

70 

40  5 

0   8 

80 

8.0 

800 

80 

46  3 

0   9 

90 

5    4 

540 

17.0 

1,700 

90 

52.0 

0.0 

0 

4.6 

460 

14.0 

1,400 

30.0 

3,000 

100 

57.8 

1.4 

140 

11.0 

1,100 

26.0 

2,600 

48.0 

4,800 

110 

63.6 

5,7 

570 

20.0 

2,000 

43.0 

3,300 

70.0 

7,000 

120 

69.4 

13.0 

1,300 

33.0 

3,300 

63.0 

6,300 

96.0 

9,600 

130 

75.1 

22.0 

2,200 

47.0 

4,700 

88.0 

8,800 

125.0 

12,500 

140 

80.9 

35.0 

3,500 

65.0 

6,500 

116.0 

11,600 

158.0 

15,800 

150 

86.7 

51.0 

5,100 

86.0 

8,600 

149.0 

14,900 

196.0 

19,600 

Far  approximating  the  storm  loss  consider 

e0  =  0.80  per  cent,  of  its  value  in  fair  weather. 
Then  p  =  0.042(e  -  0.8  X  52.0) 2  =  0.042  (e  -  41.6)2 

This  will  give  an  idea  of  the  maximum  storm  loss;  it  assumes  a  storm 
over  the  whole  line  at  the  same  time,  a  condition  that  is  most  unlikely  to 
occur.  The  storm  loss  will  also  generally  be  less  due  to  lower  temperatures. 


CORONA  CALCULATIONS  FOR  TRANSMISSION  LINES  207 

The  loss  on  a  transmission  line  will  vary  from  day  to  day  de- 
pending upon  the  temperature  and  weather  conditions.  The 
above  losses  are  calculated  for  summer  temperature,  for  winter 
the  losses  would  be  much  lower. 

Safe  and  Economical  Voltages. — It  will  generally  be  found  that 
it  is  safe  and  economical  to  operate  a  line  up  to,  but  not  above,  the 
fair  weather  e0  voltage  (determined  for  average  barometer  and 
77  deg.  F.).  This  gives  a  loss  during  storms  of  about  4.75  kw. 
per  mile  in  the  problem  considered,  but  it  is  not  likely  that  the 
storm  will  extend  over  the  whole  line  at  one  time.  Storm  during 
cold  weather  will  cause  much  less  loss  than  the  above.  It  thus 
is  generally  more  economical  to  pay  for  the  storm  loss  during 
small  parts  of  the  year  rather  than  to  try  to  eliminate  it  by  an 
excessive  conductor. 

Thus  for  the  above  line  a  desirable  operating  voltage  is  in  kilo- 
volts  between  lines  (1000  ft.  elevation) : 

e0  X  1.73  =  54.2  X  1.73  =  93.8 
(10,000  ft.  elevation) 

e0  X  1.73  =  38.4  X  1.73  =  66.5 

It  is  undesirable  to  operate  the  conductors  above  the  glow  point 
as  there  is  likely  to  be  considerable  chemical  action  on  the  con- 
ductor surface. 

Excessive  corona  loss  may  introduce  undesirable  harmonics 
in  voltage  and  current.  Fig.  113  shows  quite  large  triple  fre- 
quency current.  It  is  not  probable,  however,  that  there  will  be 
serious  harmonics  or  chemical  action  with  economical  loss. 

Methods  of  Increasing  Size  of  Conductors. — The  corona  start- 
ing voltage  is  increased  by  increasing  the  diameter  of  the  con- 
ductor. Thus,  with  the  same  amount  of  copper  a  hollow  tube 
would  give  a  higher  corona  voltage. 

A  hemp  center  conductor  is  not  reliable. 

For  the  same  resistance  an  aluminum  conductor  has  about  a 
25  per  cent,  greater  diameter  than  a  copper  conductor  and  thus, 
approximately,  25  per  cent,  higher  corona  voltage. 

In  order  to  still  further  increase  the  advantage  of  aluminum,  a 
steel-core  aluminum  cable  has  been  put  into  operation  in  Cali- 
fornia at  150  to  180  kv.  The  critical  voltage  may  also  be  de- 
creased by  grouping  together  conductors  of  the  same  potential. 

Conductors  not  Spaced  in  Equilateral  Triangle. — In  three  phase 
problems,  it  has  been  assumed  that  the  conductors  are  arranged  in 
an  equilateral  triangle.  When  the  conductors  are  not  spaced  in 
equilateral  triangle  but,  as  is  often  the  case  in  practice, 


208  DIELECTRIC  PHENOMENA 

symmetrically  in  a  plane,  corona  will  start  at  a  lower  voltage  on 
the  center  conductor,  where  the  stress  is  greatest,  than  on  the 
outside  conductor. 

The  actual  critical  voltage  for  the  center  conductor  will  be 
approximately  4  per  cent,  lower,  and  for  the  two  outer  conductors 
6  per  cent,  higher,  than  the  value  for  the  same  s,  in  the  equi- 
lateral triangle  arrangement. 

If  a  triangle  is  used  where  there  is  considerable  difference 
between  Si,  s^  and  s3,  an  exact  calculation  of  the  stress  should  be 
made.  Such  a  calculation  is  quite  complicated.  (See  Example 
Case  12,  page  234.) 

Voltage  Change  along  Line. — For  long  lines  the  voltage,  and 
therefore  the  corona  loss,  will  vary  at  different  parts  of  the  line. 
This  may  be  allowed  for  in  a  long  line  by  calculating  the  loss  per 
mile  at  a  number  of  points.  If  a  curve  is  plotted  with  these 
points  as  ordinates  and  length  of  line  as  abscissa  the  average  ordi- 
nate  may  be  taken  as  the  loss  per  mile.  The  area  of  the  curve  is 
the  total  loss.  A  line  operating  very  near  the  corona  voltage  may 
have  no  loss  at  load,  but  when  the  load  is  taken  off  there  may  be 
considerable  loss  due  to  the  rise  in  voltage.  This  may  sometimes 
be  advantageous  in  preventing  a  very  large  rise  in  voltage  when 
the  load  is  lost.  Grounding  one  conductor  will  also  cause  con- 
siderable loss  on  a  line  operating  near  the  corona  voltage  by  in- 
creasing the  stress  on  the  air  at  the  conductor  surface. 

Agreement  of  Calculated  Losses  and  Measured  Losses  on 
Commercial  Transmission  Lines. — It  is  generally  difficult  to 
make  an  exact  comparison,  as  in  most  cases  where  losses  have  been 
measured  on  practical  lines  all  of  the  necessary  data,  such  as 
temperature  along  line,  barometric  pressure,  voltage  rise  at  the  end 
of  line,  etc.,  have  not  been  recorded.  A  range  of  voltage  extend- 
ing considerably  above  ev  is  necessary  to  determine  the  curve. 
It  is  not  generally  possible  to  place  such  high  voltages  on  practical 
lines. 

The  several  examples  given  are  ones  in  which  it  has  been  pos- 
sible to  obtain  sufficient  data  to  make  a  comparison.  In  Fig. 
173  the  drawn  curve  is  calculated  from  the  formulae  for  the  tem- 
perature, barometric  conditions,  etc.,  under  which  measurements 
were  made.  The  crosses  represent  the  measured  values.  This 
agreement  between  measured  and  calculated  losses  is  very  inter- 
esting, as  it  is  for  a  long  three-phase  line  at  very  high  altitude.1 
(Note  that  the  greater  part  of  the  curve  is  below  ev.)  In  Fig. 

1  Some  of  the  first  measurements  on  practical  lines  were  made  by  Scott 
and  Mershon,  at  high  altitudes  in  Colorado.  See  A.  I.  E.  E.,  1898. 


CORONA  CALCULATIONS  FOR  TRANSMISSION  LINES  209 


174  are  similar  comparisons  on  a  single-phase  line  at  different 
frequencies.  These  measurements  were  made  before  corona  was 
a  factor  in  practical  transmission.  An  exact  agreement  could  not 
be  expected,  as  the  wave  shape  was  not  known  and  was  probably 
not  a  true  sine  wave.  Another  rather  interesting  comparison  is 
made  in  a  recent  publication  describing  the  system  of  the  Au 
Sable  Electric  Co.1  The  line  of  No.  0  copper  cable  is  125  miles  long. 
With  140  kv.  at  the  generating  end,  the  voltage  at  the  far  end  is 
165  kv.  Thus  the  loss  per  mile  is  greater  at  the  far  end  than  at 
the  generating  end.  The  average  calculated  loss  per  mile  is  15 
k\y.  The  article  states  that  the  actual  average  loss  by  prelimi- 
nary rough  measurements  was  15  to  20  kw.  per  mile.  The  above 
examples  are  given  to  illustrate  how  well  the  formulae  may  be 


1700 
1600 
1500 
1400 
1300 
1200 

Miioo 

§1000 

I 

C 

V 

/ 

1 

/ 

1 

|  800 
o  700 
M  600 
500 
400 
300 
2.00 
100 
n 

1 

/ 

l\ 

/ 

/ 

/ 

<*0 

/ 

I 

/ 

X 

0         90       100      110       120      130 

Effective  Kilo-Volts  Between  Lines 


34 
32 
30 

28 
26 

.524 
ri 
•322 

-20 
?18 
!l6 
|14 
612 

3  10 

8 

< 

4 
2 
n 

\ 

1 

>'J  C 

,ycl 

BS 

/ 

I 

/ 

I 

/ 

h 

Cy 

lea 

I 

/' 

1 

I 

/ 

1    t 

7 

1 

/ 

.  / 

/ 

/ 

t 

V 

/ 

f  / 

, 

/ 

/  - 

/ 

/ 

'/ 

Effective  Kilo-Volts 


FIG.  173.  FIG.  174. 

Comparison  of  calculated  and  measured  losses. 

FIG.  173. — Leadville.  Three  phase.  (Test  made  by  Faccioli.)  1/0 
weathered  cable.  Spacing  (flat)  124"  (314cm.).  Diameter,  0 . 95  cm.  Length 
of  line,  63.5  miles  (one  conductor).  Temp.,  11°  C.  Bar., 60cm.  Frequency, 
60—.  Curve  calculated,  x  measured. 

FIG.  174. — Outdoor  experimental  line.  (Tests  by  A.  B.  Hendricks,  Pitts- 
field,  1906.)  Wire  conductor.  Diameter,  0.064"  (radius  0.081  cm.). 
Spacing,  48"  (132  cm.).  Length,  about  800  ft.  5  =0.97. 

applied  in  the  predetermination  of  the  corona  loss  of  commercial 
transmission  lines.2 

The  Corona  Limit  of  High-voltage  Transmission,  with  Tables. 
— The  question  is  often  asked,  what  is  the  limiting  distance  im- 

1  N.  E.  L.  A.,  June,  1912. 

2  Peek,  F.  W.,  Jr.     Comparison  of  Calculated  and  Measured  Corona  Loss, 
A.  I.  E.  E.,  Feb.,  1915. 


210 


DIELECTRIC  PHENOMENA 


posed  on  high-voltage  transmission  by  the  corona  limit  of  vol- 
tage? In  the  first  place  it  does  not  seem  at  present,  except  in  very 
rare  instances,  that  corona  will  be  the  limiting  feature  at  all. 
The  limiting  feature  will,  in  all  probability,  be  an  economic  one; 
the  energy  concentrated  naturally  at  any  given  point  will  be 
exceeded  by  the  demand  in  the  surrounding  country  before  the 
transmission  distance  becomes  so  great  that  voltages  above  the 
corona  limit  are  necessary.  A  quarter  of  a  million  volts  may  be 
used  (except  at  high  altitude)  without  an  excessive  conductor 
diameter  or  spacing  (See  Tables  LXXX,  LXXXI  and  LXXXII.)1 

TABLE  LXXX. — CORONA  LIMIT  OF  VOLTAGE  2 

Stranded  Cables 
Kilo  volts  between  Line  Three-phase  Sea  Level  and  25  deg.  C. 


Size  B.  &  S. 
or  cir.  mils 

Diameter, 
inches 

Spacing,  feet 

3 

4 

5 

6 

8 

10 

12 

14 

16 

20 

4 

0.230 

56 

58 

60 

62 

64 

66 

68 

69 

71 

3 

0.261 

62 

65 

67 

70 

72 

74 

76 

77 

80 

2 

0  290 

71 

73 

76 

79 

81 

83 

85 

87 

1 

0.330 

79 

81 

85 

88 

91 

93 

95 

97 

o 

0  374 

90 

95 

98 

102 

104 

108 

109 

•     00 

0  420 

98 

104 

108 

111 

114 

117 

121 

000 

0.470 

114 

118 

121 

124 

127 

132 

0000 

0  530 

125 

130 

135 

-138 

141 

146 

250,000 

0.590 

138 

144 

149 

152 

156 

161 

300,000 

0.620 

. 

151 

156 

161 

165 

171 

350,000 

0.679 

161 

166 

170 

175 

180 

400,000 

0.728 

171 

176 

180 

185 

192 

450  000 

0  770 

178 

184 

190 

194 

200 

500,000 

0.818 

188 

194 

199 

205 

210 

800,000 

1.034 

234 

241 

244 

256 

1,000,000 

1  152 

256 

264 

270 

281 

1 

1 

1  These  tables  will  give  an  approximate  idea  of  the  voltage  limit  imposed 
by  corona.     In  general  it  will  be  found  advisable  to  operate  at  or  below  the 
e0  voltage.     Above  e0  the  storm  loss  becomes  an  important  factor.     Cal- 
culations should  generally  be  made  from  formulae  for  each  special  case. 

To  find  the  voltage  at  any  altitude  multiply  the  voltage  found  above  by 
the  5  corresponding  to  the  altitude,  as  given  in  Table  LXXXII. 

2  Kilovolts  between  lines  corresponding  to  e0  at  25  deg.  C.  and  76  cm.  ba- 
rometer.    Conductors  arranged  in  an  equilateral  triangle. 


CORONA  CALCULATIONS  FOR  TRANSMISSION  LINES  211 


TABLE  LXXXI. — CORONA  LIMIT  OF  VOLTAGE  l 
K;l  --  'Its  between  Line  Three-phase  Sea  Level  and  25  deg.  C. 

WIRES 


Size  B.  &  S. 
Cir.  Mils. 

Diameter, 
inches 

Spacing,  feet 

3 

4 

5 

6 

8 

10 

12 

14 

16 

20 

4 

0.204 

51 

54 

56 

58 

60 

62 

64 

65 

66 

68 

3       . 

0.229 

59 

62 

64 

66 

68 

70 

72 

74 

76 

2 

0.258 

69 

70 

74 

76 

78 

80 

82 

84 

1 

0.289 

75 

77 

81 

83 

86 

88 

90 

92 

0 

0.325 

85 

89 

92 

95 

97 

99 

102 

00 

0.365 

94 

98 

102 

105 

107 

110 

113 

000 

0  410 

109 

113 

116 

11Q 

121 

~\?4 

0000 

0.460 

120 

125 

128 

131 

134 

138 

To  find  the  voltage  at  any  altitude  multiply  the  voltage  found  above 
by  the  5  corresponding  to  the  altitude,  as  given  in-  Table  LXXXIL 

For  single  phase  or  two  phase  find  the  three-phase  volts  above  and  multi- 
ply by  1.16. 

TABLE  LXXXIL — ALTITUDE  CORRECTION  FACTOR  AT  25  deg.  C. 


Altitude,  feet 

a 

Altitude,  feet 

d 

0 
500 
1,000 

1.00 
0.98 
0.96 

5,000 
6,000 
7,000 

0.82 
0.79 
0.77 

1,500 
2,000 
2,500 

0.94 
0.92 
0.91 

8,000 
9,000 
10,000 

0.74 
0.71 

0.68 

3,000 
4,000 

0.89 
0.86 

12,000 
14,000 

0.63 
0.58 

Corona  is  generally  thought  of  as  affecting  only  very  high 
voltage  transmission  lines  and  of  little  other  practical  importance. 
It  may,  however,  exist  at  almost  any  voltage,  as  it  depends  not 
only  upon  voltage  but  also  upon  the  configuration  of  the  electrode 
and  the  spacing.  It  will  exist  in  cables,  on  insulators,  coils, 

1  Kilovolts  between  lines  corresponding  to  e0  at  25  deg.  C.  and  76  cm.  ba- 
rometer. 


212  DIELECTRIC  PHENOMENA 

switches,  etc. ;  in  short  wherever  air  is  present,  and  where  damage 
may  be  done  by  mechanical  bombardment  of  small  streamers, 
and  by  electrochemical , action  (ozone  and  nitrous  oxide),  unless 
means  are  taken  to  prevent  it.  In  most  cases  its  prevention  is 
fairly  simple.  This  is  further  treated  in  Chapter  X. 


CHAPTER  X 

PRACTICAL   CONSIDERATION  IN  THE   DESIGN   OF  APPARATUS 

WHERE  SOLID,  LIQUID  AND  GASEOUS  INSULATIONS 

ENTER  IN  COMBINATION 

As  important  as  the  quality  of  the  dielectric  is  the  configuration 
of  it  and  of  the  electrodes.  It  is  also  of  importance  in  combining 
dielectrics  of  different  permittivities  to  see  that  one  does  not 
weaken  the  other  by  causing  unequal  division  of  stress.  It  is 
possible  to  cause  breakdown  in  apparatus  by  the  addition  of  good 
insulation,  dielectrically  stronger  than  the  original  insulation. 

Case  1.  Breakdown  Caused  by  the  Addition  of  Stronger 
Insulation  of  Higher  Permittivity. — As  an  example  take  two 


Air 


Pressboard 


FIG.  175. — Causing  break-down  by  the  addition  of  insulation. 

parallel  plates  rounded  at  the  edges  and  placed  2  cm.  apart  in 
air,  as  in  Fig.  175 (a). 

(1)  Apply  60  kv.  (max.)  between  the  plates.  The  gradient 
then  is  60/2  =  30  kv./cm.  max.  (neglecting  flux  concentration 
at  edges).  As  a  gradient  of  31  kv./cm.  max.  is  required  to  rup- 
ture air  there  is  no  breakdown. 

14  213 


214  DIELECTRIC  PHENOMENA 

(2)  Remove  the  voltage  and  insert  between  the  plates  a  sheet 
of  pressboard  0.2  cm.  thick,  as  in  Fig.  175(6).  The  constants 
of  pressboard  are 


k  =     4  rupturing  gradient  =  175  kv./cm.  max. 

lp  =  0.2  cm. 
For  air 

k  =     1  rupturing  gradient  =  31  kv./cm. 

Apply  now  the  same  voltage  as  before.  The  addition  of  the 
pressboard  of  higher  permittivity  has  increased  the  capacity  of 
the  combination  and,  therefore,  the  total  flux  and  the  flux  density 
in  the  air.  The  gradient  has  also  been  increased.  The  combina- 
tion may  be  considered  as  two  condensers  in  series. 

Where  Ci  =  capacity  of  air  condenser,  c2  =  capacity  of  press- 
board  condenser;  e\  —  voltage  across  the  air  condenser,  e2  = 
voltage  across  the  pressboard  condenser;  the  total  flux  is 

c2e2 

k2A 
=  -—  e2 


£  ki  k2 

therefore,     -=-  e\  =  -7- 

ll  L2 


ll 

e  =  e2  + 

5<- 

k2\        k2e 


ki  k2  , 

r  ei  =  T  (e  - 
Li  L2 


Qi 


~  ki/h  +  k2/l2 
=  60  -  58.4  =  1.6 
ei  k2e 


_ 
~ 


Then  ° 


1X0.2  +  4X8  '         ' 

The  air  breaks  down  as  g\  is  higher  than  the  critical  gradient, 
causing  breakdown  of  air.  As  the  broken  down  air  is  conducting, 
most  of  the  applied  voltage  is  placed  on  the  pressboard.  Thus, 
after  the  air  ruptures,  the  gradient  on  the  pressboard  is: 

fiO 
g'2  =  -     =  300  kv./cm.  max. 


CONSIDERATION  IN  THE  DESIGN  OF  APPARATUS     215 

This  is  much  greater  than  the  rupturing  gradient  of  pressboard 
and  causes  it  to  break  down.  Therefore,  the  2.0-cm.  space, 
which  is  safe  with  air  alone,  is  broken  down  by  the  addition  of 
stronger  insulating  material  of  higher  permittivity.  The  stresses 
on  this  combination  could  have  been  calculated  directly  from 
(16a),  Chapter  II. 

Another  and  convenient  way  of  looking  at  this  is  as  follows: 

.„.  volts 

Flux 


"flux  resistance"  or  "elastance" 

S  is  termed  the  elastance  and  is  the  reciprocal  of  permittance. 
The  reciprocal  of  the  permittivity  is  termed  the  elastivity. 
For  the  given  electrode  arrangement,  S  is  proportional  to  the 
elastivity  and  the  length,  as  long  as  lines  of  force  are  practically 
straight  lines.  Let  the  relative  elastivities  be 

Air  =1.0 

Pressboard  =  0.25 

Let  the  absolute  elastivity  of  the  air  be  o-0,  and  introduce  for 
the  sake  of  abbreviation  a  =  <ra/A,  where  A  is  the  area. 

Then  the  elastances  for  the  different  circuits  in  the  test  are: 

(a)  Air  (2  cm.)  Si  =  a  X  2     X  1        =  2a 

(6)  Pressboard  (0.2  cm.)  Sp  =  a  X  0.2  X  0.25  =  0.05a 

(c)  Air  (1.8  cm.)  Sa  =  a  X  1.8  X  1        =  1.8a 

(d)  1.8  cm.  air  +  0.2  cm.  pressboard  S   =  Sp  +  Sa  =  1.85a 

Thus  when  there  is  only  air  in  the  gap 

60       30 
^  =  2a  =   ^ 

When  0.2  cm.  of  air  is  removed  and  the  same  thickness  of  press- 
board  added,  the  total  elastance  is  less  and  the  flux  increases  or 

60      _  o2.5 
**    =  i.85o  ~      a 

The  "drop"  across  the  air  is 

oo  r 

fa  XSa=  ^  X  1.85a  =  58.4  kv. 
The  "drop"  across  the  pressboard  is 

00    C 

fa  x  SP  =  ^~  X  0.05a  =  1.6  kv. 


216 


DIELECTRIC  PHENOMENA 


58.4  kv.  is  sufficient  to  cause  1.8  cm.  of  air  to  break  down. 
When  the  air  breaks  down  the  full  60  kv.  appears  across  the 
pressboard  which,  in  turn,  breaks  down. 

The  case  discussed  above  is  an  exaggerated  example  of  condi- 
tions often  met  in  practice.  In  many  power  stations  little  bluish 
needle-like  discharges,  called  "  static,"  may  be  noticed  around 
generator  coils,  bushings,  etc.  This  "  static"  is  simply  over- 
stressed  or  broken  down  air,  but  unlike  Case  1,  the  solid  dielectric 
is  sufficiently  thick  so  that  very  little  extra  stress  is  put  upon  it 

by  the  broken  down  air.  Damage 
may  be  caused  in  the  course  of  time, 
however,  by  local  heating,  chemical 
bombardment,  etc. 

Case  2.  Static  or  Corona  on  Gen- 
erator Coils.  —  Consider  the  terminal 
coil  of  a  13,200-volt  generator,  insu- 
lated by  0.25  cm.  of  built-up  mica 
(k  =  4),  and  0.45  cm.  of  varnished 
cambric  (k  =  5).  In  the  slot  is  an 
armor  of  0.1-cm.  horn  fiber  (k  =  2.5). 
In  series  with  these  is  more  or  less 
air;  assume  0.05  cm.  for  the  purpose 
of  this  calculation.  A  section  of  the 
coil  assembled  in  the  machine  is  shown 
in  Fig.  176.  The  stress  on  the  air 

may  be  approximately  found  by  assuming  the  conductors  as  one 
flat  plate  of  a  condenser,  and  the  frame  as  the  other. 

Then:  Kilovolts  between  lines  13.20  eff. 

Kilovolts  to  neutral  7  .  63  eff. 

Kilovolts  to  neutral  10  .  7    max. 
e 

9air  == 


— Copper 
—Mica 

Varnished  Cloth 
—  Horn  Fiber 
e-Air 
-  Iron 


FIG.  176. — Corona  on  genera- 
tor coils. 


*A 
kj 


(16a) 


10.7 


0.25    ,    0.45        01 


h 


~ 


10.7 
0.242 


5          2.5 

=  44  kv./cm.  max. 


0.05\ 
17 


Since  the  disruptive  strength  of  air  is  31  kv./cm.,  it  will  break 
down,  forming  corona.     Experience  has  shown  that  in  time  the 


CONSIDERATION  IN  THE  DESIGN  OF  APPARATUS     217 

corona  eats  away  the  insulation  by  mechanical  bombardment, 
local  heating,  and  chemical  action,  and  ultimately  a  short  circuit 
results. 

Assume  that  the  machine  is  operated  at  8000  volts.  The  air 
is  then  stressed  to  26.7  kv./cm.  and  corona  does  not  form.  How- 
ever, should  one  phase  become  grounded,  the  voltage  of  the 
other  two  above  ground  would  become  8.0  kilovolts  instead  of 
4.62  kilovolts,  the  gradient  on  the  air  would  rise  to  46.3  kv./cm., 
and  corona  would  result.  Assume  now  that  there  are  no  grounds, 
but  that  the  machine,  which  shows  no  corona  at  8.0  kilovolts  at 
sea  level,  is  shipped  to  Denver.  The  altitude  of  Denver  is  ap- 
proximately 5000  ft.  The  corresponding  barometer  is  24.5  in. 
(Fig.  172),  and  hence  the  relative  air  density  at  25  deg.  C.  is  0.82. 
At  this  density  the  disruptive  strength  of  air  is  0.82  X  30  =  25.5 
kv./cm.  The  air  around  the  coils  near  the  terminals  having  a 
gradient  of  26.7  kv./cm.  would  glow. 

Corona  on  machine  coils  may  be  prevented  by  tightly  covering 
the  surface  of  the  coil  with  a  conductor,  as  tinfoil,  and  connecting 
the  foil  to  the  iron  frame  of  the  machine;  this,  in  effect,  short 
circuits  the  air  space.  Naturally,  the  foil  should  be  slit  in  such  a 
way  as  to  prevent  it  from  becoming  a  short-circuited  turn  by 
transformer  action.  The  end  of  the  foil  should  also  be  guarded 
to  prevent  overstress. 

Case  3.  Overstressed  Air  in  Entrance  Bushings. — Assume 
that  a  %-in.  conductor,  supplying  power  at  33  kv.,  enters  a 
building  through  a  3— J^-in.  porcelain  bushing  having  a  1-in. 
hole  (see  diagram  Fig.  177).  The  voltage  between  the  rod  and 
the  ground  ring  is  19  kv.  The  stress  on  the  air  at  the  surface 
of  the  rod  is: 

ri  =  0.375  in.  ki  =  1 

TZ  =  0.5  in.  kz  =  4 

R  =  1.75  in. 


Qair    = 7—  — ™-  (17) 


19  X  1.41 


1 

=  120  kv./in. 
or  47.5  kv./cm.  max. 


fe  1.33    .    loge  3.5> 

+  — T — 


218 


DIELECTRIC  PHENOMENA 


To  cause  corona  on  a  rod  of  this  size  a  gradient 

0.3 

rt 

0.3 


=  31  M  + 
=  31/^1  + 


;) 


V  0.375  X  2. 
=  40.5  kv./cm.  max. 


FIG.  177. — Corona  in  bushing. 

is  necessary.  Hence,  in  the  case  considered,  there  will  be  corona, 
and  chemical  action  on  the  rod  which  will  become  coated  with  a 
green  surface  of  copper  nitrate.  The  obvious  cure  for  this  is  to 
coat  the  inside  of  the  porcelain  shell  with  a  conductor  and  con- 
nect it  to  the  rod. 

Corona  or  "static"  is  often  noticed  where  insulated  cables 
come  through  a  wall  or  bushing.  For  instance,  three  rubber 
covered  cables  may  come  through  three  bushings  in  a  wall.  If 
the  voltage  is  high  enough  a  glow  will  appear  around  the  rubber 
in  the  air  space  inside  the  bushing.  Ozone  attacks  rubber  very 
rapidly.  Such  cables  may  soon  be  broken  down  by  this  simple 
cause.  Such  breakdowns  are  often  ascribed  to  "high  frequency." 
The  remedy  is  to  "short  circuit  the  air  space."  In  doing  this  by 
metal  tubes  slit  lengthwise,  to  prevent  eddy  loss  in  the  metal, 
care  must  be  taken  to  bell  the  ends  of  the  tube,  otherwise  the  air 
will  be  stressed  where  the  metal  tube  ends.  The  "belled"  part 
may  be  filled  with  solid  insulation. 

Case  4.  Graded  Cable. — Assume  that  three  insulations  are 
available,  all  of  exactly  the  same  dielectric  strength,  but  of  per- 
mittivities as  follows: 

Insulation  A,  k  =  5.4 
Insulation  B,  k  =  3.6 
Insulation  C,  k  =  2.0 
Rupturing  gradient,  g  =  100  kv./cm. 

Assume  th.at  it  is  desired  to  insulate  a  1.0-cm.  wire  using  1.75 
cm.  of  insulation  with  an  outside  lead  cover.  The  best  way  of 


CONSIDERATION  IN  THE  DESIGN  OF  APPARATUS     219 

applying  the  insulation  is  so  that  each  part  is  stressed  in  propor- 
tion to  its  respective  strength.     This  ideal  cable  is  impossible, 
but   the  more  nearly  this  condition  is  realized  the  higher  the 
voltage  that  may  be  applied  to  the  cable  without  rupture, 
(a)  Using  insulation  A  alone  the  breakdown  voltage  is 

e  =  gr  loge  R/r  =  75  kv. 

This  is  the  same  for  either  B  or  C  alone. 

(6)  Using  insulation  A  next  to  the  wire,  then  B,  then  C,  with 


75  kv  133  kv  63  kv 

a  b  c 

FIG.  178.— Graded  cable. 

(a)  Not  graded,     (b)  Insulations  properly  arranged,     (c)  Insulations 
improperly  arranged.     Noted  break-down  voltage  in  each  case. 

thicknesses  0.25  cm.,  0.6  cm.,  and  0.9  cm.  respectively,  as  in 
Fig.  1786,  the  rupturing  voltage  is 

e  =  133  kv. 

(c)  Using  the  insulations  in  the  reverse  order  as  in  Fig.  178c  the 
rupturing  voltage  is 

e  =  63  kv. 

Note  that  the  area  in  Fig.  178a,  6,  and  c  represents  the  voltage, 
and  therefore  the  rupturing  voltage  if  the  maximum  g  is  the  rup- 
turing gradient.  This  example  is  given  to  show  how  important  it 
is  to  properly  arrange  insulations.  In  general  the  insulation  of  the 
highest  permittivity  should  be  placed  where  the  field  is  densest. 
This  applies  not  only  to  cables  but  all  electrical  apparatus.  In 
spite  of  the  fact  that  all  of  the  above  insulations  had  the  same 
dielectric  strength,  and  the  same  total  thickness,  the  rupturing 
voltages  with  the  different  arrangement  were  133  kv.,  75  kv.,  and 
63  kv.  respectively.  (Use  equation  (17).) 

Case  5.     Bushing. — Other  cases  where  the  principle  of  put- 
ting insulation  of  high  permittivity  at  points  of  dense  field  is 


220 


DIELECTRIC  PHENOMENA 


shown  are  illustrated  in  Figs.  18  and  179.  The  solid  insulation  of 
the  lead  in  Fig.  18,  because  its  contour  follows  the  lines  of  force, 
does  not  increase  the  stress  on  the  air  near  it.  It  is,  for  that 
reason,  much  better  than  an  insulator  which  has  the  insulation 
arranged  in  such  a  way  that  the  stress  on  the  air  is  increased  in 
the  denser  part  of  the  field.  However,  by  inserting  the  high 

permittivity  insulation  in  the  dense 
fields  at  the  rod,  and  cutting  it 
away  in  the  middle,  a  better  ar- 
rangement is  obtained  (Fig.  179). 
In  the  zone  between  flux  lines  a  and 
b,  there  is  now  the  insulation  of  high 
permittivity,  and  air  of  low  per- 
mittivity, in  series  in  the  same  way 
as  in  the  graded  cable,  and  with 
the  same  effect.  In  tests  the  insu- 
lation of  the  type  of  Fig.  179  arced 
over  at  18  per  cent,  higher  voltage 
than  that  of  Fig.  18  (of  same  over- 
all dimensions) ,  though  its  air  path 
was  6.5  per  cent,  shorter.1 

In  practice  it  is  generally  neces- 
sary to  add  corrugations  to  increase 
the  " leakage  path"  on  account  of 
dirt  settling   on   the   surface,  etc. 
The  " ideal"  design  is  not  always 
the  best  in  practice. 
Case  6.     Transformer  Leads  or  Bushings. — One  of  the  most 
common  bushings  is  the  oil  filled  type.     In  the  design  of  such  a 
bushing  two  general  problems  present  themselves:  The  internal 
stress  on  the  oil,  which  determines  the  puncture  voltage;  the 
external  stress  on  the  air,  which  determines  the  arc-over  voltage. 
In  the  design  of  a  bushing,   however,   the  whole  dielectric 
circuit  must  be  considered  at  the  same  time. 

If  the  surface  of  the  shell  follows  a  line  of  force,  the  internal 
field  does  not  cut  the  shell  and  cause  flux  concentration  at 
points  on  the  shell;  the  voltage  per  unit  length  of  surface, 

1  Fortescue,  Paper,  A.I.E.E.,  March,  1913. 
Weed,  Discussion,  A.I.E.E.,  March,  1913. 

2  Figs.   18  and  179  cannot  represent  practical  leads  as  the  rod  and  torus 
field  is  changed  by  the  plane  of  the  transformer  case. 


FIG. 


179. — Bushing. 
Torus.2 


Rod   and 


CONSIDERATION  IN  THE  DESIGN  OF  APPARATUS     221 

however,  is  not  constant  with  this  condition  unless  the  lines  of 
force  are  approximately  straight  parallel  lines  A  bushing,  when 
parallel  planes  are  approximated,  theoretically,  need  not  be  over 
2  in.  high  for  a  100-kv.  arc-over.  This  imposes  a  large  diameter 
compared  to  length,  and  large  well-rounded  metal  caps,  etc. 
Such  a  bushing  would  arc  over  with  slightly  dirty  surfaces,  mois- 
ture on  surfaces,  etc.,  at  very  low  voltage.  A  practical  lead  must 
generally  be  fairly  long  and  corrugated  (See  Table  LXXVIII, 
page  190). 

Where  the  surface  follows  a  curved  line  of  force,  the  internal 
field  still  does  not  cut  the  surface  and  cause  the  so-called ' '  leakage ' ' 
by  local  flux  concentration,  but  the  gradient  is  not  constant  along 
this  line  of  force.  Local  breakdowns  precede  spark-over. 

If  the  lead  does  not  follow  a  line  of  force,  the  lines  from  the 
outside  pass  through  the  shell  to  the  inside.  In  this  case  the 
shell  should  be  so  shaped  that  the  stress  is  divided  parallel  to  the 
surface  and  also  perpendicular  to  the  surface. 

In  an  improperly  designed  bushing  of  this  sort,  breakdown 
might  occur  at  places  along  the  surface,  and  at  other  points 
out  from  the  surface.  For  instance,  as  an  extreme  case,  it  might 
be  imagined  that  the  surface  of  a  bushing  followed  an  equipo- 
tential  surface.  There  would  then  be  no  stress  in  the  direction 
of  the  surface,  but  breakdown  would  occur  by  the  stress  per- 
pendicular to  the  surfaces,  as  corona.  Conversely  a  condition 
might  obtain  which  would  cause  greatest  stress  along  the  surface 
as  when  a  line  of  force  is  followed.  As  the  surface,  due  to  dirt, 
etc.,  is  generally  weaker  than  the  air,  it  is  in  most  cases  better 
not  to  have  maximum  stress  along  it.  (See  Table  LXXVIII.) 
In  any  case  the  stress  should  be  uniform  measured  in  either  di- 
rection. Where  the  shells  follow  a  line  of  force  the  field  is  more 
readily  approximated  by  experiment,  or  by  calculation,  than 
where  the  lines  of  force  cut  the  shell,  when  flux  refraction,  etc., 
must  be  considered.  The  direction  of  the  flux  may  be  controlled 
by  the  arrangement  of  metal  parts.  The  bushing  problem  is  a 
space  problem. 

In  practice  it  is  generally  necessary  to  add  petticoats.  These 
should  be  placed  so  as  to  produce  the  minimum  disturbance 
in  the  field  with  minimum  stress  along  their  surfaces. 

Another  type  of  lead  is-  the  condenser  lead,  built  with  the 
object  of  stressing  all  of  the  solid  insulating  material  approxi- 
mately equally.  It  consists  of  a  number  of  cylindrical  condensers 


222 


DIELECTRIC  PHENOMENA 


of  equal  thickness,  but  of  unequal  lengths,  arranged  in  such  a 
way  as  to  make  the  several  capacities  equal  (Fig.  180).  If  this 
were  exactly  the  case,  the  voltages  across  the  equal  thicknesses 
of  insulation  and  equal  distances  along  with  the  surface  would 
be  equal.  This  condition  is  possible  but  not  generally  reached 
on  account  of  the  capacity  of  the  condensers  to  ground,  to  the 
central  rod,  and  to  each  other  (Fig.  180) ;  to  secure  equal  division 
of  voltage  here  (Fig.  180)  it  would  be  necessary  to  connect  the 
condenser  plates  to  proper  sources  of  potential.  The  condition 
may  be  approached,  however,  to  such  a  degree  that  a  good  prac- 
tical lead  is  the  result  when  the  insulating  has  been  carefully 
done.  A  smaller  diameter  is  obtained,  but  a  greater  length  is  re- 


FoiK 

$ 


Ground 


Surface  Break 


f 


Distributed 
Break 


Effect 

FIG.  180. — Condenser  bushing. 

quired  due  to  arcing  distance  in  the  air  (i.e.j  to  avoid  arcs  of  the 
nature  of  the  heavy  line,  Fig.  180).  The  present  practical  form 
is  a  long  thin  lead.  (One  disadvantage  claimed  is  shown  in  the 
small  sketch  accompanying  Fig.  180.)  Little  flaws  in  various 
parts  of  the  lead  are  lined  up  by  the  metal  parts  and  put  directly 
in  series.  The  separation  of  the  insulation  by  metal  is,  from  an- 


CONSIDERATION  IN  THE  DESIGN  OF  APPARATUS     223 

other  standpoint,  an  advantage.  A  progressing  corona  streamer 
is  stopped  on  reaching  the  metal  surface  at  any  layer.  Concen- 
tration of  flux  at  the  edges  of  the  metal  cylinder  must  also  be 
taken  care  of.  The  condenser  lead  is  often  arranged  with  a 
metal  hat  for  flux  control. 


FIG.  181. — Diagramatic  representation  of  flux,  and  capacities  in  condenser 

bushing. 

Case  7.  Dielectric  Field  Control  by  Metal  Guard  Rings, 
Shields,  Etc. — It  is  sometimes  practical  to  accomplish  more  with 
metal  than  by  added  insulation.  In  a  case  where  the  field  is  not 
uniform,  but  very  much  more  dense  at  one  point  than  at  another, 
the  flux  may  be  made  more  uniform  by  relieving  the  dense  por- 
tion and  distributing  over  the  less  dense  portion  by  a  proper  ar- 
rangement of  metal  parts  connected  to  a  source  of  potential  of 
the  proper  value.  This  is  not  always  practical,  as  the  necessary 
complicated  potential  connections  often  weaken  the  apparatus 
and  make  it  much  more  liable  to  breakdown. 

As  a  simple  example :  Fig.  182  represents  two  spheres  of  unequal 
size  in  air,  one  at  potential  e  the  other  at  potential  —  e,  or  a  voltage 
2e  between  them.  All  the  flux  from  A  ends  on  B.  The  flux  den- 
sity at  B  is  then  much  greater  than  at  A  and  the  air  around  B  is 
very  much  more  stressed  than  the  air  at  the  surface  of  A.  The 
equipotential  surface  C  may  be  covered  with  thin  metal  and  no 
change  takes  place  in  the  flux  at  A  or  B.  If,  however,  C  is  con- 
nected by  a  wire  to  B  the  flux  around  B  disappears  and  there  is  no 


224 


DIELECTRIC  PHENOMENA 


stress  on  the  dielectric  at  the  surface  of  B.  The  total  flux  in- 
creases because  of  the  greater  capacity  between  A  and  C.  The 
stress  at  A,  due  to  increased  flux  density,  increases,  but  it  is  still 
much  less  than  the  stress  formerly  at  B,  and  a  greater  potential 
is  required  for  spark-over.  In  other  words,  the  insulation  is  more 
uniformly  stressed  and  therefore  working  at  greater  efficiency. 

If  instead  of  surrounding  B  or 
completely  shielding  it  the  sphere 
C  be  placed  as  in  (c)  and  con- 
nected to  B  by  a  wire  the  stress 
is  relieved  at  B  and  increased  at 
A.  The  distribution  at  B  is 
again  more  uniform. 

An  actual  example  where  this 
principle  was  made  use  of  in  an 
emergency  case  several  years  ago 
by  the  author  is  illustrated  in 
Figs.  183  and  184.  In  making 
some  experiments  200  kv.  were 
carried  through  the  roof  of  a  shed 
by  porcelain  bushings.  During 
a  heavy  wind  storm  the  roof  was 
blown  off  and  one  bushing 
cracked  as  indicated  by  the 
jagged  line.  When  the  roof  was 
replaced  and  an  attempt  made 
to  put  the  bushing  again  into 
operation  it  was  found  that  bad 
arcing  took  place  to  the  damp 
wood  at  130  kv.  As  no  extra 
bushings  were  immediately  ob- 
tainable, and  it  was  necessary 
to  finish  the  experiments,  the  ex- 
pedient of  field  control  was  made 

use  of.  By  hanging  a  metal  torus  made  of  a  coil  of  wire  on 
the  rod,  the  work  of  about  fifteen  minutes,  the  bushing  was 
made  operative  up  to  200  kv.  This  was  not  as  good  as  a 
new  bushing,  not  the  best  sort  of  bushing,  but  it  was  a  means  of 
making  a  defective  bushing  operative,  and  prevented  a  shut- 
down of  a  month  or  more. 

The  effect  of  this  shield  is  shown  diagrammatically  in  Fig.  184. 


FIG.    182. — Simple    illustration 
flux  control. 


CONSIDERATION  IN  THE  DESIGN  OF  APPARATUS     225 


By  moving  the  ring  up  and  down  the  rod,  a  point  of  minimum 
flux  density  on  the  cracked  surface  of  the  porcelain  is  found.  It 
better  distributed  the  flux  and  reduced  the  maximum  flux  density 
below  the  rupturing  value. 


FIG.  183.  —  Entrance 
bushing. 


FIG.  184.  —  Making  bushing  shown  in  Fig.  183 
operative  by  flux  control  after  lower  part  had 
broken  off. 


Case  8.  High  Frequency. — Apparatus  must  be  designed  to 
meet  not  only  normal  but  also,  to  a  reasonable  extent,  abnormal 
conditions.  Due  to  surges,  lightning,  arcing  grounds,  switching, 
etc.,  high  frequency  voltages  travel  over  the  line,  say  to  a 
transformer.  The  voltage  may  not  be  increased  at  the  trans- 
former terminals,  as  the  "high  frequency"  may  exist  only  as  a 
slight  ripple  on  normal  voltage  wave.  The  lightning  arrester 
therefore  does  not  discharge, 
and  a  needle  gap  across  the 
transformer  terminals  shows 
no  voltage  rise.  A  needle  gap 
across  a  small  section  of  the 
transformer  may  indicate  a 
voltage  several  times  normal 
line  voltage.  The  points  of 

greatest    potential    difference  KHO  cycles 

will  depend  upon  the  fre-  FIG.  185. — Effect  of  "high  frequency" 
quency  and  the  transformer  ^re™ltage  distribution  across  a  coil  °f 
constants.  The  fact  that , 

"high  frequency"  may  enter  an  apparently  high  inductance 
and  build  up  high  local  potentials  is  because  the  inductance 
also  contains  capacity.  It  is  not  possible  to  give  a  theoretical 
treatment  of  this  here.  It  is  simply  mentioned  to  show  that  it 
is  sometimes  dangerous  to  thin  insulation  at  one  part  and  add  it 
at  another  in  order  to  get  perfect  flux  distribution  under  normal 
conditions,  because  under 'abnormal  conditions  great  potential 
differences  may  exist  across  the  weak  insulation.  It  also  illus- 


1 

/ 

\ 

W 

inc 

infl 

/ 

\ 

A 

0  , 

! 

T' 

3 

/ 

& 

2 

3    4 

j 

\ 

o5 

1 

olt 

si 

4 

/ 

\ 

/ 

V 

- 

~^" 

— 

— 

226  DIELECTRIC  PHENOMENA 

trates  how  "  high  frequency"  generally  is  dangerous  by  building 
up  high  local  potential  differences.  Where  a  large  number  of 
metal  parts  are  used  to  distribute  the  flux  under  normal  con- 
dition, the  effect  of  the  well-known  multi-gap  lightning  arrester 
may  come  in  and  cause  break- down  at  high  frequencies. 

It  is,  for  somewhat  similar  reasons,  not  always  best  to  follow 
ideal  designs  in  line  insulators,  leads,  etc.  The  ideal  surface  may 
be  such  as  to  make  the  surface  time  lag  low  or  the  rain  arc-over 
low. 

Case  9.  Dielectric  Field. — Draw  the  dielectric  lines  of  force 
and  equipotential  surfaces  between  two  parallel  cylinders  so  that 
J^2  of  the  flux  is  included  between  any  two  adjacent  lines  of  force, 
and  J^o  of  the  voltage  is  between  any  two  adjacent  equipotential 
circles. 

Let    S  =  10  cm.  between  conductor  centers 
r    =     1  cm.  =  conductor  radius. 

From  Chapter  II,  page  21, 


S  -  \/S*  -  4r2  =  10  -  VlOO  -  4 


The  distance  between  focal  points  of  the  lines  of  force  is 
S'  =  S  -  2z  =  10  -  0.20  =  9.80 

It  is  desired  to  include  one-twelfth  of  the  total  flux  between 
lines  of  force.  Draw  radial  lines  from  the  flux  centers  K2  X  180 
=  30  deg.  apart.  (See  Chapter  II,  pages  14  and  19.)  The  point 
of  intersection  of  a  radial  line  with  N.  N.  (Fig.  186a)  is  a  point  on 
the  line  of  force.  The  line  of  force  is  hence  a  circle  with  center 
on  N.  N.,  and  passing  through  the  point  of  intersection  of  tha 
radial  line  N.N.,  A'i,  and  A'2.  The  lines  of  force  are  therefore 
determined.  The  centers,  etc.,  might  have  been  calculated  from 
equation  (8),  page  19.  The  line  of  force  is  also  determined 
graphically  by  drawing  the  diagonal  line  through  the  intersec- 
tion of  radial  lines,  as  shown  in  Fig.  187. 

The  equipotential  surfaces  in  this  case  may  be  found  graphic- 
ally in  a  similar  way  by  drawing  diagonals  through  the  inter- 
sections of.  the  circles  of  the  component  fields.  Other  resultant 
fields  may  be  drawn  from  corresponding  plane  diagrams  if  the 


CONSIDERATION  ,IN  THE  DESIGN  OF  APPARATUS     227 

component  fields  are  given  for  the  same  strength,  or  same  poten- 
tial differences  between  the  equipotential  surfaces.  Any  number 
of  fields  may  be  so  combined,  two  at  a  time.  It  is  often  possible 
to  approximate  for  practical  purposes  the  field  of  a  complicated 
structure  by  so  combining  the  simple  fields  of  the  component 
electrodes. 


N 


f 

\ 

y     \ 

Ua 

n'                                      ^ 

;\ 
/ 

\ 

C(                                                       } 

Fig.  186  (a) 


N 


N 


Fig.  186(6) 
FIG.  186. — Method  of  drawing  lines  of  force  and  equipotential  surfaces. 


The  equipotential  surfaces  are  circles  with  centers  on  the  line 
A'i,  A' 2.     See  equation  (7),  page  18.     The  distance  of  the  center 

b*  ab 


of  the  circles  from  A'2  is  -  — F>  and  the  radius  is 


where 


5?       HI  IV  4.          t/XJ.\_/       A  dfVlJ.  U.tJ      J.O  7    ? 

a  -  b 

a  and  6  must  be  so  chosen  that  the  permittances  between  circles 
are  equal. 


228 


DIELECTRIC  PHENOMENA 


For  any  point  p  on  the  line  A'iA'2  (Fig.  1866),  the  potential  to 
the  neutral  plane  due  to  A'2  is 


Due  to  A'i,  it  is 
6lnp 


26 


.8' 


FIG.  187. — Graphical  method  of  drawing  lines  of  force  between  two 

cylinders. 


The  total  voltage  from  any  point  p  to  the  neutral  is 

!'-*) 


np 


I 


_±_          (8'  -  b) 
6np  ~  10ge "      6 


It  is  desired  to  divide  the  field  up  into  n  equal  voltages  between 
the  conductor  surface  and  the  neutral  plane.     The  potential  from 
the  conductor  to  neutral  is  en  and  is  known 
Due  to  A' 2  : 

2(r  -  z) 


CONSIDERATION  IN  THE  DESIGN  OF  APPARATUS     229 
Due  to  A'  i  : 


log 


2(S'  -  (r  -  z)) 
-       -S^ 
S'  -  (r  -  z} 


.'.   t  =2irKk 


'  -  (r  -  z) 


Let  |8  be  the  fraction  of  the  voltage  en  it  is  desired  to  place  be- 
tween the  neutral  plane  and  any  point  p  on  the  surface  under 
consideration,  then  (Fig.  1866) 


^np    — 


1  (S'  -  b) 

loge 


'  -  (r  -  0)  "  6 


In  this  problem 

loge*=  -  —  -  —  =  constant  =  F 


r  —  z 


9.8  -  (1  -  0.1)       .       8.92 

—  r^.T       =  log€  092  -  2'290 


o/   _   t 

—7  —  =  anti-log  (3F 


(anti-log  0F  +  1) 

6  is  thus  determined. 

If  it  is  desired  to  find  6  for  the  first  circle  from  the  conductor 
0  =  0.9. 

9.84          9.84 


"7.7  +  1  -   8.7 
For  the  next  circle 

0  =  0.8 

,  9.84 

=  fi  23  4-  1    ~ 

15 


' 


230 


DIELECTRIC  PHENOMENA 


Other  values  are  found  and  tabulated  in  Table  LXXXIII. 
a  and  R  are  thus  found.  The  circles  may  now  be  drawn  with 
radii  R,  centers  on  A'iA'z,  and  intersecting  A'iA'2  b  cm.  from  A'2. 

TABLE  LXXXIII. — EQUIPOTENTIAL  SURFACES 


ft 

6 

a  =  S'  -  b 

R        ab 

a-b 

ab 

R~  a-b 

1.0 

b       0.900 

8.90 

1.00 

8.00 

8.00 

0.9 

bl      1.110 

8.69 

1.27 

7.58 

9.65 

0.8 

62      1.353 

8.45 

1.62 

7.09 

11.49 

0.7 

63      1.648 

8.15 

2.07 

6.50 

13.45 

0.6 

64      1.98 

7.82 

2.65 

5.84 

15.46 

0.5 

66      2.38 

7.42 

3.50 

5.04 

17.65 

0.4 

6e      2.81 

7.09 

4.65 

4.28 

19.90 

0.3 

67      3.29 

6.51 

6.65 

3.22 

21.40 

0.2 

68      3.80 

6.00 

10.35 

2.20 

22.80 

0.1 

69      4.34 

5.46 

21.15 

1.12 

23.67 

0.0 

610     4.90 

4.90 

00 

0.00 

24.00 

F  =  2.290  =  constant     z  =  0.1      Sf  =  S  -  2.z  =  9.8 
The  gradient  at  any  point,  and  therefore  the  equigradient 
surfaces  may  be  found  as  follows: 
The  flux  density  at  any  point  is 


D  = 


Cnen  = 


(Pages  21  and  23.) 
2jrkKen 


D  = 


2S'irkKe 


9  = 


or  for  a  given  voltage,  spacing  and  size  of  conductor,  the  term  to 
the  right  is  constant,  and  it  follows : 


g  =  -    -  times  a  constant  =  - 


CONSIDERATION  IN  THE  DESIGN  OF  APPARATUS     231 


is  the  gradient  at  any  point  x\  cm.  from  A' \  and  x2  cm. 
from  A'2.  Putting  x\  in  terms  of  x%  and  the  angle  a  between 
£2  and  the  line  A'  \A'<i\ 

1 


+  S'2  -  2S'x2  cos  a. 

N 


M 


90 


FIG.  188. — Method  of  plotting  equigradient  curves. 
TABLE  LXXXIV. — EQUIGRADIENT  SURFACES 


a 

0° 

30° 

60° 

90° 

120° 

150° 

180° 

g  =21.4 

Xz    = 

1.16 

1.13 

1.07 

1.00 

0.97 

0.94 

0.93 

g  =  16.1 

X2    = 

1.64 

1.60 

1.44 

1.32 

1.27 

1.23 

1.20 

g  =  10.7 

Xz   = 

2.91 

2.85 

2.25 

2.00 

1.85 

1.75 

1.74 

g  =    8.9 

Xz    = 

4.90 

3.40 

2.71 

2.37 

2.19 

2.06 

2.02 

g  =    8.0 

Xz  = 

i 

4.0 

3.08 

2.59 

2.38 

2.26 

2.20 

g  =    5.34 

Xz    = 

4.9±4v/IIT1 

8.20 

4.70 

3.81 

3.27 

3.17 

3.10 

g  =    2.67 

X2    = 

i 

i 

8.63 

6.73 

5.83 

5.40 

5.29 

1  Such  a  gradient  does  not  exist  on  this  line  and  hence  xz  is  imaginary. 
(See  plot  Fig.  8,  page  15.) 

Gradient  at  Equidistant  Points  on  the  Conductor  Surface 


Angle  bet.  horizontal  Af\A'z 

and  line  through  point  and 

0° 

30° 

60° 

90° 

120° 

150° 

180° 

conductor  center 

g  

26  7 

26  0 

23  7 

21  6 

iq  4 

1C    0 

17  S 

232  DIELECTRIC  PHENOMENA 

(1)  Find  the  maximum  gradient  at  the  conductor  surface  for 
100  kv.  between  conductors.     This  may  be  found  directly  from 
equation  (12a),  pages  24  and  29,  and  is  26.7  kv./cm. 

(2)  Find  the  gradient  at  six  equidistant  points  on  the  con- 
ductor surface  for  100   kv.  between  conductors.     (See  Table 
LXXXIV.) 

(3)  Calculate  the  equigradient  curves  for  gradients  of  21.4, 
16.1,  10.7,  8.9,  8.0,  5.34,  and  2.67  kv.  per  centimeter  at  100  kv. 
between  conductors.     This  may  be  done  from  the  above  equation 
by  putting  g  equal  to  the  required  gradient,  and  finding  x2  for 
given  values  of  a.     The  results  are  tabulated  in  Table  LXXXIV, 
and  method  of  plotting  is  shown  in  Fig.  188. 

A  complete  plot  of  Case  9  is  shown  in  Fig.  8,  page  15.  Note 
that  in  such  a  diagram,  the  permittance  or  elastance  of  each  of 
the  small  cells  bounded  by  sections  of  lines  of  force  and  equipo- 
tential  surfaces  is  equal. 

Case  10.  Dielectric  Fields  in  Three  Dimensions. — The  field 
of  a  conductor  arrangement  which  must  be  considered  in  three 
dimensions,  as  a  rod  and  torus,  rod  through  a  plane,  etc.,  is  gen- 
erally represented  on  a  plane  figure  in  such  a  way  that  if  the  figure 
were  revolved  about  its  axis,  the  solid  would  be  formed  sur- 
rounded by  its  three-dimensional  field.  The  small  cells  of  the 
plane  figure  bounded  by  sections  of  lines  of  force  and  equipoten- 
tial  surfaces  would  form  cells  in  the  solid  of  equal  permittance. 

In  the  case  of  figures,  as  those  for  parallel  wires,  a  wire  in  a 
cylinder,  and  parallel  planes,  it  is  possible  to  represent  the  field 
by  considering  only  two  dimensions.  The  height  and  thickness 
of .  the  cells  on  the  plane  give  constant  permittance,  or  average 

.,  .  ,  =  constant.     The  third  dimension  is  then  the  length 

thickness 

of  the  wire  and  need  not  be  considered  in  drawing  these  cells. 

In  the  case  of  the  three-dimensional  field,  the  cells  on  the  plane 
must  be  of  such  a  height  and  thickness  that  the  solid  cells  have 
constant  permittance,  or  where  the  cell  is  small 

hr 

—  =  constant. 

This  can  readily  be  seen  from  Fig.  189. 

It  is  a  general  law  that  the  cells  must  be  so  arranged  that  the 
stored  energy  may  be  a  maximum  or  the  permittance  a  maximum. 
In  cases  where  the  field  need  only  be  considered  in  two  dimensions, 
it  is  thus  possible,  without  great  difficulty,  to  draw  a  field  by  a 


CONSIDERATION  IN  THE  DESIGN  OF  APPARATUS     233 


of  approximations  in  which  the  cells  have  a  cpnstant 

The  lines  of  force  must 


series 

-  or  add  up  to  maximum  permittance. 
t 


lane  Cell, 


be  normal  to  the  electrodes  and  to  the  equipotential  surfaces  at 
the  point  of  contact.  This  is  also  possible  for  a  three-dimensional 
field,  but  extremely  difficult  because  the  cells  must  be  drawn  in 
such  a  way  that  the  solid  cells  have  constant  permittance. 

The  best  way  in  which  to  determine  a  field  that  cannot  be  read- 
ily calculated  is  experimentally.  If  the  electrodes  are  immersed  in 
an  electrolyte  in  a  large  tank  made 
of  insulating  material,  and  a  small 
current  passed  between  them,  equi- 
potential surfaces  may  be  measured 
at  equal  voltage  intervals  on  a  plane 
through  the  axis  of  revolution  by 
means  of  a  galvanometer.1  These 
surfaces  correspond  to  the  dielectric- 
equipotential  surfaces.  The  lines  of 
force  may  be  drawn  at  right  angles 
to  these,  so  as  to  divide  the  field 
into  solid  cells  of  equal  capacity  (see 
above).  It  is  difficult  in  practice 
to  get  results  by  this  method  when 
the  problem  includes  several  per- 
mittivities. 

Theoretically  it  would  be  possible 
to  use  a  solid  material  to  represent, 
for  instance,  the  porcelain  shell  of  an 
insulator,  and  the  electrolyte  to  rep- 
resent the  air.     The  resistivities  of  the  two    materials  should 
then  have  the  same  ratio  as  the  elastivities  of  porcelain  and  air. 
It  is  difficult  to  find  a  solid  material  with  a  resistivity  in  the 
order  of  that  of  an  electrolyte. 

As  a  less  exact  experimental  method,  the  lines  of  force  may  be 
obtained  by  mica  filings  and  the  problem  then  solved  by  approxi- 
mations. These  methods  may  be  developed  into  very  useful 
ones  for  a  study  of  flux  control,  etc. 

Case  11.  Effect  of  Ground  on  the  Permittance  and  Gradient 
for  Parallel  Wires. — Such  problems  are  solved  by  taking  the 
"images"  symmetrically  below  the  ground. 

1  Fortesque  has  described  this  method.    See  A.I.E.E.,  March,  1913.    Much 
more  exact  results  may  be  obtained  than  those  shown  in  this  paper. 
Rice,  Solution  of  Electrostatic  Problems,  A.I.E.E.,  March,  1917. 


FIG. 


Formed 
Plane  GeU 


189.— Dielectric    field 
three  dimensions. 


in 


234  DIELECTRIC  PHENOMENA 

Voltages  between  AB  due  A}  B,  AI,  B\  are 

,    *   V.        8 

&A  ~    i 


~  (2irkK>  10ge  S    /S  s  S'  where  the  wires  \ 

loge    —    >  are  far  aPart<  ' 


«*i    =    + 


The  total  voltage  is 


,      S  .  .       2h\         t     .      S2h 
log-  +  loge  -)  =  ^^  log  -  - 


Q    —  L.    —        """"• 

r   a 
Where  the  wires  are  far  apart  the  gradient  is 

e 

g  ~  S    2h 

r     a 

The  problem  for  a  number  of  wires  may  be  solved  in  the  same 
way.  The  fluxes  from  the  different  wires  may  then  not  be  the 

same  and  the  solution  is  more 
~~^L5  difficult  as  a  number  of  simul- 

/]  taneous  equations  must  be  writ- 

'  I  ten  and  solved. 

Case  12.  Three-phase  Di- 
electric Field  with  Symmetrical 
and  Unsymmetrical  Spacings. — 

|      /  \  The  fluxes  between  conductors 

/    \  j '  °n  a  three-phase  line  vary  sinu- 

/         \  |  soidally  with  the  voltages.    The 

instantaneous  values  of  voltages 
may  be  added  algebraically  as 

Fio.  190 .^Effect  of  ground  on  ca-  above'     The  effective  or  maxi- 
pacity  between  parallel  wires.         mum  values  are  found  by  geo- 
metrical addition. 

To  illustrate:  find  the  fluxes  for  three  three-phase  conductors 
in  an  equilateral  triangle,  and  also  for  flat  spacing.  In  order  to 
greatly  simplify  the  problem,  the  effects  of  ground  or  " images" 
will  be  neglected,  and  the  conductors  considered  far  apart. 


VI 


i  ^ 

\l  \l 

~~       image® 


CONSIDERATION  IN  THE  DESIGN  OF  APPARATUS     235 

Then  due  to  fluxes  from  I 

A          \          B          |          C 

1  AB  r  CB 

(a)  EAB  =  ^-r^  WA  loge  -  -  +  ^loge^r  +  tc  l°&  TTJ)  =e  sin  0 


e  sin  (0  -  120) 

Only  two  of  the  three  equations  which  may  be  written  as 
above  are  independent,  since  the  sum  of  the  voltages  must  be 
zero.  The  other  independent  equation  is 

(c)  *A  +  ts  +  tc  =  0 

A 

o 
Conductors  Spaced  in  a  Triangle  o       o  (equilateral  triangle). 

B      C 

Substituting  spacing  S  in  (a)  and  (b)  and  solving  for  \f/A,  \j/B, 
and  \j/c 

(1.5  sin  0  +  0.866  cos  0) 


Let         e(1.5  sin  0  +  0.866  cos  6)  =  e0  (sin  B  —  a) 
put  0  =  90  and  9  =  0  and  solve  for  ea  and  a 


.  . 

sin  (0  -  150)  =  -       —~  sm  (0  -  150) 


.  . 

(0  -  30)  =  -  o       sin  (0-30) 


^c  may  be  found  in  the  same  way,  or  for  this  particular  case, 
$A>  $B>  an(i  tc  are  equal  by  symmetry. 
For  single  phase: 

2irkKe 

Y    —   ~  o 

2  log^ 

Therefore,  when  the  wires  are  far  apart,  and  with  the  same  voltage 

2 
between  lines,  the  three-phase  stress  is  —  ^  times  the  single-phase 

stress. 


236  DIELECTRIC  PHENOMENA 

Flat  Spacing  A  B  C—  Putting  S,  S,  and  2S  in  a  and  b  and 
o   o  o 

solving  as  before, 

2irkKe 
*B  =  ~  -jp-  -sin  (0-150) 

V3  log*  --  -  0.58  log  2 

2irkKe 
=  ~          — «—      -  sin  (0  -  150) 

V3  loge  5  -  0.4 
The  flux,  and  therefore  the  stress,  when  the  wires  are  far  apart, 

a 

is  greatest  on  the  middle  wire.      For  —  =  500  it  is  4  per  cent. 

greater  than  on  the  wires  with  the  same  S  and  triangular 
spacing  as  above.  \I/A,  and  \f/c  are  6  per  cent,  lower  than  for 
the  triangular  spacing.  The  gradients  vary  in  the  same  way. 
Corona,  therefore,  starts  on  the  center  wire  at  a  4  per  cent, 
lower  voltage,  and  on  the  outer  wires  at  a  6  per  cent,  higher  volt- 
age than  for  triangular  spacings. 

Case  13.  Occluded  Air  in  Insulation. — It  is  interesting  to 
estimate  the  effect  of  occluded  air  in  solid  insulation.  Assume 
that  in  the  process  of  manufacture  air  bubbles  have  formed  in  a 
sheet  of  rubber  insulation.  The  sheet  is  1  cm.  thick.  The  "  bub- 
bles" are  thin  compared  to  the  rubber,  and  long  in  the  direction  of 
the  length  of  the  sheet.  It  is  estimated  that  the  largest  ones  are 
0.01  cm.  thick,  and  0.1  cm.  long  and  wide.  The  electrodes  which 
the  rubber  insulates  may  be  assumed  as  being  practically  parallel 
planes.  The  working  voltage  is  40  kv.,  or  the  stress  is  40  kv./cm. 
effective  in  the  rubber.  As  the  air  bubbles  are  not  thick  enough 
to  greatly  disturb  the  field,  the  same  flux  passes  through  the  air  as 
through  the  rubber.  The  permittivity  of  the  rubber  is  3.  The 
stress  on  the  air  is,  therefore,  3  X  40  =  120  kv./cm.  effective. 
Air  breaks  down  at  21.2  kv./cm.  effective  at  atmospheric  pres- 
sure. It  seems  probable  that  these  bubbles  will  break  down, 
even  after  allowance  is  made  for  the  extra  strength  of  thin  films, 
and  a  possible  pressure  higher  than  atmospheric.  See  pages 
61,  196  and  appendix.  It  is  probable  that  the  solid  insulation 
would  soon  break  down  on  account  of  heat  and  chemical  action. 

Case  14.  General. — (a)  Estimate  the  visual  corona  voltage 
when  wires  are  wet.  Compare  with  the  visual  corona  voltage 
when  wires  are  dry. 


CONSIDERATION  IN  THE  DESIGN  OF  APPARATUS     237 

Calculate  gv  from  the  formula  on  page  67,  Chapter  III. 
Insert  the  value  in  formula  (20).  Maximum  ev  to  neutral  is  thus 
found.  If  the  voltage  used  is  a  sine  wave,  reduce  to  effective  kv. 
by  dividing  by  \/2.  For  a  three-phase  line  the  voltage  between 
wires  may  be  found  by  multiplying  by  \/3;  for  a  single-phase  line, 
by  multiplying  by  2.  Compare  with  dry  visual  critical  voltage 
calculated  from  equation  (20)  ;  page  43. 

(6)  At  what  voltage  will  the  above  wires  spark  over  wet  and 
dry  single  phase;  three  phase? 

Estimate  dry  spark-over  voltage  from  equation  given  on  page 
83,  Chapter  IV.  Estimate  wet  arc-over  voltage  by  assuming 
needle  gap  spark-over. 

(c)  Calculate    the   dry   arc-over    curve   for  a   10-cm.   sphere 
(grounded)  at  5  =  0.90,  and  spacings  from  1.5  to  10  cm. 

Use  equation  (136),  Chapter  IV.  Estimate  a  wet  spark-over 
curve  as  outlined  for  spheres  on  page  105,  Chapter  IV. 

(d)  What  is  the  voltage  required  to  puncture  0.5  cm.  of  paper 
insulation  when  the  time  of  application  is  limited  to   1/100 
second?     In  100  seconds? 

Use  equation  on  page  179,  Chapter  VII,  of  the  form 


es  =  ga  X  thickness. 

(e)  Estimate  the  loss  per  cubic  centimeter  at  1000  cycles  in  a 
piece  of  varnished  cambric,  at  5.0  kv./mm.,  25  deg.  C.  Use 
equation  page  185,  Chapter  VII. 

(/)  What  is  the  breakdown  gradient  of  a  piece  of  porcelain 
2  cm.  thick? 

0.94 

g  =  7.5  (1  +         ) 


where  t  =  thickness  in  mm. 

g  =  gradient  in  kv./mm.  (eff.) 

(See  Chapter  VII,  page  174.) 


DATA  APPENDIX 


1.  MEASURED  CORONA  LOSS 
Indoor  Line — 60 -cycle 

The  current  and  watts  given  are  measured  values  due  to  corona, 
divided  by  the  total  conductor  length  in  kilometers.  Corrections 
have  been  made  for  transformer  and  leads.  The  voltage  is  given 
to  neutral.  As  these  measurements  were  made  on  a  single-phase 
line,  the  voltages  between  wires  were  twice  the  value  given.  To 
obtain  kva.  per  km.  of  conductor  multiply  amps,  per  km.  by 
volts  between  lines. 

CORONA  Loss — INDOOR  LINE — GO-CYCLE 


Test  10B 

Test  l\B 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

10  52 

0  07 

13    7 

0  33 

12.52 

0.51 

16.7 

0.92 

14.80 

1  40 

18  1 

1.11 

17  10 

3  20 

19  9 

0  070 

1.64 

18.20 

4  02 

24.7 

0.100 

3.95 

19  60 

6  83 

29  3     • 

0.150 

6.90 

22.30 
24.90 

27.20 
29.70 

0.225 
0.310 

0.395 

9.44 
15.03 

20.63 

33.2 
36.3 

39.7 
44.0 

0.189 
0.223 

0.268 
0.325 

10.40 
14.20 

18.75 
26.73 

28.00 
25  90 

0.404 
0  342 

22.40 
16  80 

47.3 
50  2 

0.380 

34.20 

23.60 
20.80 

0.263 

11.80 
7.16 

45.2 
41.5 

0.350 
0.293 

29.20 
22.20 

18.40 

4  14 

37.4 

0.238 

15.69 

16.10 

1  98 

31.0 

0.163 

8.08 

27.0 
22.3 

0.128 
0.082 

5.29 
2.53 

Spacing,  15.25  cm. 

Radius,  0.032  cm. 

Total  cond.  length,  0.0838  km. 

6  =  1.02. 


Spacing,  30.5  cm. 

Radius,  0.032  cm. 

Total  cond.  length,  0.0838  km. 

5  =  1.02. 


238 


DATA  APPENDIX 


239 


Test  13J5 

Test  15B 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

19.5 

0.051 

0.96 

17.3 

0.35 

24.3 

0.071 

1.78 

23.7 

0.059 

1.17 

29.6 

0.099 

3.23 

30.2 

0.078 

2.34 

34.0 

0.133 

4.95 

36.1 

0.109 

3.92 

38.0 

0.146 

6.49 

42.2 

5.76 

43.0 

9.13 

49.8 

0.166 

9.26 

46.7 

0.196 

12.51 

56.7 

0.200 

13.21 

52.4 

0.224 

16.35 

62.5 

0.223 

16.70 

57.5 

21.00 

66.5 

0.246 

20.00 

62.5 

0.285 

26.25 

71.4 

24.35 

68.3 

0.327 

34.40 

78.6 

0.310 

30.95 

73.1 

0.359 

40.60 

84.4 

0.322 

37.20 

79.1 

0.385 

50.50 

89.4 

0.345 

41.90 

84.0 

59.50 

95.4 

50.50 

90.0 

0.430 

72.00 

99.3 

0.395 

58.60 

93.6 

0.460 

83.10 

91.0 

0.369 

45.60 

102.0 

0.510 

93.40 

81.6 

0.310 

34.10 

67.9 

21.55 

52.1 

0.177 

10.46 

39.1 

0.126 

4.44 

27.0 

0.068 

1.74 

Spacing,  61  cm. 

Radius,  0.032  cm. 

Total  cond.  length,  0.0838  km. 

5  =  1.03. 


Spacing,  91.5  cm. 

Radius,  0.032  cm. 

Total  cond.  length,  0.0838  km. 

8  =  1.012. 


240 


DIELECTRIC  PHENOMENA 


Test  20B 

Test  21  B 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

Eff.  kv.  to 

neutral,  en 

1 

Amp.  per 
km. 

Loss 
kw./km.,  p 

17   8 

0.21 

19.8 

0.81 

24  6 

1  29 

24  5 

1  15 

30  1 

2.17 

27.2 

.     2.02 

36.2 

0.110 

3.71 

30.7 

2.19 

42  0 

0  128 

5.16 

34.8 

3.42 

47.0 

0.159 

6.94 

39.8 

0.129 

3.86 

53.2 

0.190 

9.80 

44.8 

0.156 

5.04 

62.0 

0.233 

14.60 

50.4 

0.177 

6.47 

67.6 

0.258 

19.23 

55.1 

0.212 

8.45 

73.4 

0.273 

21.12 

60.6 

0.234 

10.80 

78.1 



26.70 

64.6 

0.246 

12.40 

85.2 

0.346 

33.10 

70.0 

0.266 

15.10 

93.2 

0.385 

42.70 

77.9 

0.310 

19.30 

100  2 

51.70 

87.6 

26.60 

87  0 

0  350 

35.60 

94.3 

32.60 

76  1 

0  298 

25  00 

101  5 

41.00 

65.2 

0.250 

15.95 

49.4 

0.178 

7.44 

40.1 

0.114 

4.55 

Spacing,  122  cm. 

Radius,  0.032  cm. 

Total  cond.  length,  0.0421  km. 

5  =  1.018. 


Spacing,  183  cm. 

Radius,  0.032  cm. 

Total  cond.  length,  0.0342  km, 

5  =  1.012. 


DATA  APPENDIX 


241 


Test  22B 

Test  24B 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

20  7 

0.72 

20.1 

0  24 

24  5 

1  01 

25  3 

0  98 

27.2 

1.21 

32.0 

1.84 

30.9 

1.98 

36  0 

0  103 

3  18 

34.6 
40.1 
45.2 

0.100 
0.121 
0.149 

2.34 
3.57 
4.53 

41.0 
45.7 
50.3 

0.120 
0.138 

4.52 
6.11 
8.30 

50.3 
55  1 

0.171 

5.71 
7  43 

57.0 

62  2 

0.185 
0  210 

11.57 
15  10 

60.2 
64.6 
69  5 

0.215 
0.230 

9.13 
11.05 
11  99 

67.3 

72.4 
77  5 

0.240 
0.266 
0  290 

19.15 
23.20 
27  50 

78  5 

16  37 

82  3 

32  10 

87.5 
94.2 

0.345 
0.380 

23.00 
26  00 

87.8 
92  5 

37.90 
43  80 

103.2 

0.417 

34.50 

97.3 

50.80 

100  5 

55  60 

79.0 

28  70 

65.0 

17  10 

52.7 

9.90 

Spacing,  274.5  cm. 
Radius,  0.032  cm. 
Total  cond.  length,  0.0342  km. 
5  =  1.012. 


Spacing,  91.5  cm. 

Radius,  0.057  cm. 

Total  cond.  length,  0.0818  km. 

5  =  1.0009. 


242 


DIELECTRIC  PHENOMENA 


Test  265 

Test  28B 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

20.0 

0.37 

10  6 

23.2 

0.053 

0.98 

14.2 

29.0 

2.24 

16.1 

0  18 

32.8 

3.36 

18.4 

0  43 

37.1 

0.124 

5.14 

20.2 

0.98 

41.1 

0.141 

6.60 

22.2 

0.061 

1.34 

46.7 

0.173 

9.90 

24.0 

0.069 

1.83 

51.3 

0.202 

12.32 

25.0 

0.072 

2.20 

57.1 

0.232 

18.30 

27.0 

0:087 

2.93 

61.1 

0.262 

22.30 

30.2 

0.120 

5.00 

66.2 

0.290 

28.40 

34.0 

0.157 

7.88 

72.0 

0.332 

36.60 

36.7 

0.178 

10.30 

75.7 

0.334 

40.80 

36.7 

0.181 

10.10 

80  7 

50  50 

40  7 

0  212 

14  80 

85.0 

0.413 

56.50 

44.5 

0.265 

20.30 

88.7 

0.431 

64.00 

47.1 

0.298 

24.80 

91.0 

0.464 

71.40 

51.7 

0.369 

35.20 

96.5 

0.515 

83.40 

49.6 

0.342 

30.80 

101.0 

0.562 

104.00 

43.0 

0.251 

18.20 

82.8 

0.396 

54.50 

' 

74.7 

0.333 

39.00 

69  7 

33  00 

60.0 

0.255 

22.70 

Spacing,  0.61  cm. 

Radius,  0.057  cm. 

Total  cond.  length,  0.08186  km. 

5  =  1.002. 


Spacing,  30.5  cm. 

Radius,  0.057  cm. 

Total  cond.  length,  0.0818  km. 

5  =  0.993. 


J* 


DATA  APPENDIX 


243 


Test  305 

Test  32B 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 

kw./km.,  p 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

21.7 

0.18 

22.5 

0.21 

25.6 

0.92 

27.2 

0.049 

0  31 

31.5 

.     2.45 

32.5 

0.062 

\J  •  O  J. 

1.41 

36.2 

4.30 

37.2 

0.086 

2.70 

40.5 

0.138 

5.80 

41.1 

0.100 

3.68 

45.7 

0.156 

8.60 

45.6 

0.123 

5.03 

49.7 

0.180 

11.70 

50.3 

0.146 

7.35 

54.2 

0.204 

15.30 

55.0 

0.178 

10.18 

59.5 

0.238 

19.50 

60.0 

0.194 

13.50 

64.0 

0.269 

24.60 

65.7 

0.222 

17.40 

68.2 

0.290 

29.70 

72.0 

0.257 

23.20 

73.0 

0.322 

36.30 

77.2 

0.278 

27.60 

78.5 

0.352 

45.20 

82.5 

0.298 

31.40 

83.5 

0.384 

54.00 

89.2 

40.00 

88.2 

0.441 

63.00 

92.2 

44.00 

95.0 

0.486 

76.00 

85.2 

35.80 

96.5 

0.500 

81.20 

70.0 

20.80 

100.0 

0.530 

92.00 

61.7 

14.32 

103.0 

0.600 

114.30 

90.2 

0.459 

60.20 

79.5 

0.356 

45.30 

75.2 

0.319 

38.60 

65.5 

26.20 

51.7 

13.40 

Spacing,  61  cm. 

Radius,  0.071  cm. 

Total  cond.  length,  0.0815  km. 

5  =  0.98. 


Spacing,  91.5  cm. 

Radius,  0.914  cm. 

Total  cond.  length,  0.0815  km. 

6  =  1.002. 


244 


DIELECTRIC  PHENOMENA 


Test  33B 


Test  41 B 


Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

:  Eff.  kv.  to 

neural,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

24.7 

0.31 

28.3 

29   8 

1.53 

35.5 

0.071 

2.72 

32  6 

2  45 

41  0 

0  108 

4  90 

35  6 

3  50 

48  6 

0  184 

10  40 

39  3 

4.96 

53.7 

0.208 

13  25 

43  7 

6  37 

59  0 

0  234 

17  50 

47  5 

9.57 

63.8 

0.265 

23.40 

51  5 

12.9 

69.4 

0.306 

30.02 

56.3 

60  2 

15.5 

20.8 

73.6 
71.9 

0.353 
0.325 

35.70 
34.10 

65  5 

34  8 

60.1 

0.244 

19.85 

67.0 

29.6 

54.2 

0.210 

13.65 

54  4 

15.3 

59.9 

0.250 

19.35 

57.0 
47.0 

0.224 
0.161 

16.30 

8.87 

Spacing,  61  cm. 

Radius,  0.0914cm. 

Total  cond.  length,  0.0815  km. 

5  =  1.006. 


Spacing,  61  cm. 

Radius,  0.105  cm. 

Total  corid.  length,  0.0423  km. 

5  =  1.001. 


DATA  APPENDIX 


245 


Test  455 

Test  475 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 

kw./km..  p 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

22  3 

0.06 

45.0 

0.080 

0.37 

25.8 
29  7 

0.12 
0.34 

50.0 
54.5 

0.100 
0.104 

0.74 
1.90 

35  7 

1.41 

60.5 

5.76 

39  5 

2.70 

65.7 

0.152 

9.13 

44  2 

4.78 

70.5 

0.174 

12.60 

50  2 

8.10 

75.5 

0.205 

16.30 

54  0 

10.70 

79.0 

0.230 

18.75 

59  5 

14  70 

87  0 

26  80 

64  5 

19.50 

9-1.7 

31.40 

69.0 

74  0 

24.80 
30.10 

96.5 
93.5 

0.321 

38.20 
34.10 

79  7 

37  20 

90  0 

29  80 

82  7 

43  40 

82  0 

21  70 

88  7 

56  20 

75  8 

16.20 

98  0 

59  00 

58  0 

4  22 

99  7 

80  50 

42  6 

0.49 

103  0 

84  50 

40  0 

0  24 

86  7 

52  20 

75.5 

32.70 

Spacing,  61  cm. 

Radius,  0.164  cm. 

Total  cond.  length,  0.0185  km. 

5  =  0.996. 


Spacing,  91.5  cm. 

Radius,  0.256  cm. 

Total  cond.  length,  0.0815  km. 

5  =  0.996. 


16 


246 


DIELECTRIC  PHENOMENA 


Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

44.1 

0.61 

40.5 

I  16 

47.2 
51  7 



1.11 

3  87 

44.5 
43  0 

3.13 

2  27 

64.5 

5.90 

46.8 

5.70 

60  8 

10  60 

50.6 

12  30 

67  2 

17  15 

55  6 

19  25 

71.5 

20.70 

58.8 

75  5 

26.70 

53.8 

16  05 

81.7 

33.30 

49.6 

9.70 

76  6 

27.10 

45.7 

5.27 

78  5 

29.40 

43  2 

2.82 

74.0 

23.90 

39.3 

1.23 

69  5 

18  30 

68.0 

16.55 

58  2 

8.10 

52  7 

4.10 

Spacing,  61  cm. 

Radius,  0.256  cm. 

Total  cond.  length,  0.0815  km. 

5  =  1.00. 


Spacing,  30.5cm. 

Radius,  0.256  cm. 

Total  cond.  length,  0.0815  km. 

d  =  0.996. 


DATA  APPENDIX 


247 


Test  515 

Test  545 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Loss 
kw./km.,  p 

Eff.  kv.  to 
neutral,  en 

Amp.  per 
km. 

Losa 
kw./km.,  p 

«0     K 

0    l^Q 

9  15 

25  5 

0  051 

fiC    A 

0  190 

14  55 

31  8 

72  0 

0  220 

20  10 

37  7 

0  06 

70  o 

0261 

28  45 

42  7 

0  30 

07   Q 

0  318 

40  20 

47  1 

0  30 

91  5 

49  70 

57.0 

0.49 

co  n 

34  60 

63  2 

1  03 

72  8 

22  10 

69  7 

1.81 

56  0 

5  65 

76.5 

0.152 

5.08 

61  5 

10  20 

78.7 

0.164 

6.48 

67.2 
70.2 



15.75 
19.30 

84.5 

89.3 
95.0 
99.1 
102  2 

0.184 

0.210 
0.238 
0.263 

12.22 

17.20 
23.90 
28.40 
31.90 

97.2 

26.00 

92  0 

20  90 

87  0 

16  50 

76.7 

82.0 
72.1 

5.82 

9.10 
2.67 

Spacing,  61  cm.  Spacing,  91.5cm. 

Radius,  0.333  cm.  Radius,  0.464  cm. 

Total  cond.  length,  0.0817  km.  Total  cond.  length,  0.0825  km. 

5  =  0.999.  5  =  0.982. 

All  of  the  above  tests  were  taken  at  a  temperature  of  about  25  deg.  C. 

MEASURED  CORONA  LOSS 

Outdoor  Line — 60  cycle 

Columns  1,  2,  and  3  are  actual  measured  values  and  include 
transformer  and  lead  losses.  Column  4,  the  actual  corona  loss, 
for  the  length  of  line  used  in  the  test  is  obtained  from  Column  3 
by  subtracting  transformer  and  lead  losses. 

These  tests  were  made  on  comparatively  long  single-phase  lines 
out  of  doors,  and  the  conductor  surfaces,  etc.,  were  not  in  as  good 
condition  as  in  the  case  of  the  indoor  line.  Transformer  losses 


248 


DIELECTRIC  PHENOMENA 


for  several  temperatures  are  given.     The  voltage  values  are  ef- 
fective between  lines. 


Test  No.  146,  Line  AI 

Test  No.  18,  Line  A 

Kv.  bet. 
lines 

Amp. 

Kw. 

Kw.  line 
loss,  p 

Kv.  bet. 
lines 

Amp. 

Kw. 

Kw.  line 
loss,  p 

63.5 

0.056 

0.07 

0.01 

80.0 

0.040 

0.12 

0.01 

80.5 

0.077 

0.12 

0.02 

90.0 

0.100 

0.16 

0.02 

90.1 

0.092 

0.15 

0.02 

101.1 

0.107 

0.20 

0.04 

107.5 

0.113 

0.30 

0.12 

112.0 

0.113 

0.25 

0.05 

115.2 

0.121 

0.35 

0.14 

121.6 

0.123 

0.30 

0.06 

126.2 

0.135 

0.63 

0.37 

129.5 

0.131 

0.35 

0.07 

134.2 

0.146 

0.85 

0.55 

140.0 

0.146 

0.49 

0.16 

142.5 

0.154 

1.29 

0.95 

150.0 

0.160 

0.76 

0.38 

150.0 

0.164 

1.95 

1.45 

160.0 

0.172 

1.60 

1.17 

158.0 

0.173 

2.69 

2.25 

152.0 

0.162 

0.90 

0.51 

166.1 

0.185 

4.00 

3.48 

164.2 

0.174 

2.00 

1.55 

165.0 

0.183 

3.51 

3.02 

172.0 

0.187 

3.40 

2.90 

173.7 

0.196 

5.00 

4.45 

183.2 

0.205 

5.60 

5.02 

163.4 

0.184 

2.70 

2.23 

188.2 

0.210 

6.92 

6.30 

170.4 

0.193 

4.20 

3.67 

196.4 

0.223 

9.02 

8.42 

181.0 

0.198 

6.06 

5.42 

202.2 

0.237 

11.06 

10.36 

203.0 

0.251 

12.84 

12.04 

206.0 

0.242 

12.90 

12.09 

199.2 

0.243 

11.50 

10.73 

187.2 

0.211 

6.95 

6.34 

193.4 

0.227 

9.10 

8.49 

196.4 

0.225 

9.60 

8.90 

176.4 

0.197 

4.74 

4.17 

Total  conductor  length,  109,500cm. 

165.6 

0.184 

2.70 

2.21 

Spacing,  310  cm. 

162.8 

0.180 

2.38 

1.81 

No.  3/0  7-strand  hard-drawn  copper- 

154.4 

0.169 

1.28 

0.85 

weathered  cable,  diam.  1.18  cm. 

166.0 

0.176 

2.94 

2.45 

Temperature,  wet,  16  deg.  C. 

dry,  18.5. 

184.4 

0.198 

6.49 

5.87 

Barometer,  75.5  cm. 

172.0 

0.193 

3.85 

3.31 

Bright  sun,  wind. 

160.0 

0.177 

2.03 

1.57 

Test  No.  146,  Line  A 

146.2 

0.162 

0.80 

0.42 

Total  conductor  length,  109,500  cm. 

Spacing,  310  cm. 

138.0 

0.150 

0.52 

0.19 

No.  3/0  7-strand  cable,  dia.  1.18  cm. 

127.6 

0.137 

0.40 

0.12 

Temperature,  wet,  24  deg.  C. 

122.5 

0.129 

0.33 

0.08 

dry,  30  deg.  C. 

111.2 

0.117 

0.25 

0.04 

Barometer,  75.7  cm. 

101.0 

0.105 

0.20 

0.03 

Hazy. 

1  This  curve  was  taken  after  the  line  had  been  standing  idle  over  a  month  in  the 
summer.  The  "going  up"  points  show  an  excess  loss  due  to  dust  and  dirt  on  the  conductor. 
This  disappears  at  high  voltage  and  does  not  show  in  the  "coming  down"  readings. 


DATA  APPENDIX 


249 


Test  No.  102 

Kv.  bet. 
lines 

Amp. 

Kw. 

Kw.  line 
loss,  p 

201.0 

0.232 

6.05 

6.65 

211.0 

0.277 

9.10 

8.63 

189.0 

0.210 

3.54 

3.19 

181.8 

0.200 

2.36 

2.04 

170.8 

0.189 

1.10 

0.80 

160.0 

0.176 

0.60 

0.36 

149.0 

0.162 

0.36 

0.16 

201.0 

0.231 

6.15 

5.75 

149.0 

0.162 

0.39 

0.19 

140.5 

0.150 

0.29 

0.12 

135.5 

0.145 

0.25 

0.10 

124.5 

0.131 

0.20 

0.08 

113.5 

0.118 

0.16 

0.08 

102.3 

0.103 

0.13 

0.07 

Total  conductor  length,  109,500  cm. 

Spacing,  310  cm. 

No.    3/0    7-strand    H.    D.  copper- 

weathered  cable,  diam.  1.18  cm. 

Temperature,  wet,  1 

dry,  1 

Barometer,  7.47  cm. 

Cloudy. 

250 


DIELECTRIC  PHENOMENA 


Test  No.  84,  Line  A 

Test  No.  105,  Line  A 

Kv.  bet. 
lines 

T..              Kw.  line 
Amp.            Kw. 

loss,  p 

Kv.  bet. 
lines 

Amp. 

Kw. 

Kw.  line 
loss,  p 

120.0 

0.138       0.24       0.15 

79.8 

0.080 

0.03 

0.01 

129.0 

0.150       0.30       0.19 

90.7 

0.093 

0.04 

0.01 

160.0 

0.175       0.78       0.61 

101.5 

0.106 

0.06 

0.02 

181.0 

0.202       3.65       3.40 

109.5 

0.114 

0.08 

0.03 

189.0 

0.212       4.65       4.36 

120.6 

0.127 

0.10 

0.04 

203.0 

0.237       7.84       7.48 

130.0 

0.139 

0.14 

0.06 

213.0 

0.252      11.20      10.78 

141.5 

0.154 

0.19 

0.09 

205.0 

0.239       8.70       8.18 

147.0 

0  .  165 

0.21 

0.08 

153.6 

0.168 

0.25 

0.12 

Total  conductor  length,  108,500cm. 

159.0 

0.178 

0.30 

0.16 

Spacing,  310  cm. 

169.8 

0.199 

0.51 

0.35 

No.  3/0  7-strand  cable  (H.  D.  copper- 

174.0 

0.190 

0.70 

0.53 

weathered),  1.18  cm. 

Temperature,  wet,  1  deg.  C. 

181.0 

0.198 

1.20 

1.02 

dry,  3  deg.  C.       . 

186.2 

0.204 

1.74 

1.55 

Barometer,  75.2  cm. 

192.6 

0.212 

2.70 

2.49 

Cloudy. 

200.6 

0.221 

4.00 

3.77 

208.6 

0.237 

5.60 

5.34 

216.0 

0.247 

7.40 

7.13 

221.0 

0.259 

9.00 

8.70 

227.0 

0.271 

11.00 

10.66 

234.0 

0.288 

13.60 

13.25 

189.0 

0.210 

2.30 

2.10 

195.0 

0.217 

3.10 

2.88 

203.8 

0.229 

4.96 

4.72 

212.0 

0.242 

6.70 

6.44 

, 

219.0 

0.257 

8.60 

8.31 

Total  conductor  length,  109,500  cm. 

Spacing,  310  cm. 

No.    3/0    7-strand    H.    D.  copper- 

weathered  cable,  diam.  1.18  cm. 

Temperature,  wet,  13  deg.  C. 

dry,  13  deg.  C. 

Barometer,  76.2  cm. 

Bright  sun,  no  wind,  snow  on  ground. 

DATA  APPENDIX 


251 


Test  No.  100,  Line  B 

Test  No.  73,  Line  B 

Kv.  bet. 
lines 

Amp. 

Kw. 

Kw.  line 
loss,  p 

Kv.  bet. 
lines 

Amp. 

Kw. 

Kw.  line 
loss,  p 

67.0 

0.02 

0.02 

43.0 

0.016 

77.0 

0.025 

0.03 

0.02 

60.0 

0.022 

88.0 

0.028 

0.05 

0.02 

69.7 

0.026 

0.08 

0.06 

98.9 

0.035 

0.07 

0.03 

80.6 

0.030 

0.10 

0.07 

109.5 

0.040 

0.12 

0.07 

90.5 

0.034 

0.15 

0.11 

119.5 

0.043 

0.22 

0.14 

101.5 

0.038 

0.30 

0.26 

128.0 

0.050 

0.42 

0.32 

91.0 

0.034 

0.09 

0.05 

137.0 

0.054 

0.90 

0.78 

90.5 

0.034 

0.10 

0.06 

144.0 

0.060 

1.94 

1.80 

70.3 

0.026 

0.06 

0.04 

161.2 

0.078 

4.50 

4.31 

101.6 

0.038 

0.17 

0.12 

153.0 

0.070 

3.04 

2.88 

101.6 

0.038 

0.17 

0.12 

173.8 

0.090 

6.60 

6.47 

109.5 

0.041 

0.40 

0.36 

185.0 

0.103 

8.72 

8.36 

105.5 

0.040 

0.14 

0.09 

200.0 

0.106 

11.90 

11.59 

115.0 

0.040 

0.14 

0.09 

185.0 

0.103 

8.76 

8.50 

115.0 

0.0425 

0.88 

0.82 

159.0 

0.078 

4.10 

3.92 

121.5 

0.048 

0.16 

0.09 

139.0 

0.058 

1.22 

1.10 

126.5 

0.053 

2.00 

1.93 

161.2 

0.080 

4.70 

4.51 

130.5 

0.055 

2.48 

2.40 

211.8 

0.135 

14.80 

14.46 

140.5 

0.064 

3.70 

3.61 

144.5 

0.073 

4.26 

4.16 

Total  conductor  length,  29,050  cm. 

70.5 

0.03 

0.00 

Spacing,  91.4  cm. 

91.5 

0.030 

0.06 

0.02 

0.375-in.     galv.    steel   cable,    diam. 

106.0 

0.038 

0.18 

0.13 

0.953cm. 

150.0 

0.078 

4.80 

4.69 

Temperature  wet,  1  deg.  C. 

dry,  1  deg.  C. 

156.4 

0.083 

5.80 

5.68 

Barometer,  74.7  cm. 

161.0 

0.089 

6.72 

6.67 

Cloudy. 

166.0 

0.093 

7.50 

7.36 

Total  conductor  length,  29,050  cm. 

Spacing,  91.4  cm. 

• 

0.23-in.    galv.    steel    cable,    diam. 

0.585  cm. 

Temperature  wet,  1  deg.  C. 

dry,  3  deg.  C. 

Barometer,  75.2  cm. 

Cloudy. 

252 


DIELECTRIC  PHENOMENA 


Test  No.  79,  Line  B 

Test  No.  80,  Line  B 

Kv.  bet. 
lines 

Amp. 

Kw. 

Kw.  line 
loss,  p 

Kv.  bet. 
lines 

Amp. 

Kw. 

Kw.  line 
loss,  p 

213.0 

0.105 

8.64 

8.38 

81.0 

0.029 

0.07 

0.04 

205.0 

0.010 

7.68 

7.40 

91.0 

0.032 

0.09 

0.05 

202.0 

0.094 

7.40 

7.13 

100.5 

0.035 

0.12 

0.07 

186.0 

0.088 

6.00 

5.80 

110.5 

0.038 

0.16 

0.11 

181.0 

0.081 

5.00 

4.80 

120.5 

0.041 

0.40 

0.34 

168.4 

0.072 

3.96 

3.81 

130.5 

0.048 

1.30 

1.22 

159.6 

0.063 

3.00 

2.88 

139.5 

0.055 

2.25 

2.17 

150.0 

0.058 

2.24 

2.13 

153.0 

0.067 

3.20 

3.09 

138.0 

0.048 

1.14 

1.06 

160.0 

0.075 

4.40 

4.28 

120.0 

0.043 

0.20 

0.14 

172.0 

0.084 

5.70 

5.54 

120.0 



0.26 

0.20 

181.0 

0.094 

7.00 

6.82 

110.0 

0.071 

0.19 

0.14 

192.0 

0.103 

8.50 

8.28 

99.0 

0.068 

0.13 

0.09 

199.0 

0.109 

9.40 

9.15 

213.0 

0.124 

11.70 

11.38 

Total  conductor  length,  29,050  cm. 

Spacing,  244  cm. 

Total  conductor  length,  29,050  cm. 

0.23-in.  galv.  steel  cable,  diam.  0.585 

Spacing,  152  cm. 

cm. 

0.23-in.    galv.     steel    cable,    diam. 

Temperature,  wet,  1  deg.  C. 

0.585  cm. 

dry,  3  deg.  C. 

Temperature,   wet,  1  deg.  C. 

Barometer,  72.5  cm. 

dry,  3  deg.  C. 

Cloudy. 

Barometer,  72.5  cm. 

Cloudy. 

DATA  APPENDIX  253 

CORONA  Loss — OUTDOOR  LINE — GO-CYCLE 


Test  No.  125,  Line  B 

Test  No.  126,  Line  B 

Kv.  bet. 
lines 

Amp. 

Kw. 

Kw.  line 
loss,  p 

Kv.  bet. 
lines 

Amp. 

Kw. 

Kw.  line 
loss,  p 

80.0 

0.025 

0.06 

0.05 

100.0 

0.031 

0.12 

0.09 

88.0 

0.031 

0.13 

0.11 

110.0 

0.037 

0.22 

0.17 

101.0 

0.037 

0.32 

0.29 

119.0 

0.041 

0.44 

0.36 

110.0 

0.041 

0.74 

0.68 

131.0 

0.050 

1.36 

1.22 

120.0 

0.050 

1.67 

1.59 

142.0 

0.056 

2.38 

2.16 

128.0 

0.056 

2.56 

2.44 

151.0 

0.065 

3.23 

2.92 

140.0 

0.067 

4.00 

3.80 

160.0 

0.074 

4.20 

3.78 

150.0 

0.08 

5.42 

5.12 

171.0 

0.082 

5.45 

4.93 

159.6 

0.09 

6.86 

6.46 

181.0 

0.09 

6.56 

5.89 

168.4 

0.101 

8.30 

7.80 

194.0 

0.102 

8.20 

7.34 

181.0 

0.112 

10.36 

9.68 

202.0 

0.111 

9.26 

8.30 

190.0 

0.122 

12.24 

11.44 

212.0 

0.117 

10.84 

9.74 

201.0 

0.134 

14.68 

13.61 

222.0 

0.128 

12.44 

11.18 

213.0 

0.148 

17.28 

16.14 

231.0 

0.135 

13.80 

12.38 

206.0 

0.144 

15.76 

14.72 

225.0 

0.129 

12.88 

11.58 

196.6 

0.128 

13.60 

12.70 

217.0 

0.124 

11.64 

10.45 

186.2 

0.117 

11.44 

10*69 

205.0 

0.112 

9.70 

8.70 

175.0 

0.103 

9.20 

8.59 

196.6 

0.104 

8.56 

7.68 

165.6 

0.096 

7.76 

7.27 

186.6 

0.096 

7.32 

6.56 

153.4 

0.083 

5.92 

5.57 

176.0 

0.086 

6.12 

5.51 

143.0 

0.074 

4.56 

4.33 

165.0 

0.078 

4.96 

4.49 

134.0 

0.064 

3.34 

3.18 

156.4 

0.069 

3.96 

3.59 

123.0 

0.053 

2.00 

1.90 

142.4 

0.056 

2.46 

2.24 

114.0 

0.044 

1.00 

0.94 

134.0 

0.051 

1.60 

1.45 

104.0 

0.038 

0.38 

0.34 

125.0 

0.044 

0.82 

0.71 

Total  conductor  length,  29,050  cm.  . 

Total  conductor  length,  29,050  cm. 

Spacing,  91.4  cm. 

Spacing,  183  cm. 

No.  4  H.  D.  copper  wire,  diam.  0.518 

No.   4    H.    D.   copper  'wire,   diam. 

cm. 

0.518  cm. 

Temperature,  wet,  5.0  deg.  C. 

Temperature,  wet,  5.0  deg.  C. 

dry,  4.6  deg.  C. 

dry,  4.5  deg.  C. 

Barometer,  75.9  cm. 

Barometer,  75.9  cm. 

Cloudy,  slight  breeze. 

Cloudy,  slight  breeze. 

254 


DIELECTRIC  PHENOMENA 


Test  No.  137,  Line  B 

Test  No.  138,  Line  B 

Kv.  bet. 
lines 

Amp. 

Kw. 

Kw.  line 

loss,  p 

Kv.  bet. 
lines 

Amp. 

Kw. 

Kw.  line 
loss,  p 

80.0 

0.05 

0.02 

79.2 

0.06 

0.03 

90.5 

0.025 

0.11 

0.06 

91.2 

0.025 

0.12 

0.07 

100.5 

0.029 

0.35 

0.26 

99.9 

0.027 

0.26 

0.18 

110.7 

0.037 

0.95 

0.78 

111.4 

0.036 

0.08 

0.65 

121.0 

0.044 

1.42 

1.19 

120.8 

0.039 

1.22 

1.06 

131.0 

0.051 

2.11' 

1.76 

121.5 

0.049 

1.90 

1.59 

141.5 

0.056 

2.70 

2.26 

141.0 

0.055 

2.30 

2.20 

150.8 

0.064 

3.24 

2.72 

149.0 

0.059 

2.80 

2.34 

161.0 

0.072 

4.05 

3.40 

161.0 

0.066 

3.40 

2.85 

172.0 

0.078 

4.80 

4.05 

171.4 

0.074 

4.20 

3.53 

183.0 

0.084 

5.60 

4.73 

181.4 

0.079 

4.80 

4.05 

196.0 

0.093 

6.60 

5.59 

192.0 

0.085 

5.60 

4.73 

205.0 

0.102 

7.60 

6.44 

202.2 

0.092 

6.56 

5.67 

202.0 

0.098 

7.30 

6.19 

214.4 

0.11 

7.50 

6.35 

186.0 

0.087 

6.00 

5.08 

197.0 

0.089 

6.10 

5.15 

165.0 

0.075 

4.30 

3.63 

174.0 

0.076 

4.40 

3.71 

145.0 

0.061 

2.86 

2.40 

153.2 

0.063 

3.00 

2.51 

124.0 

0.047 

1.75 

1.46 

134.4 

0.051 

2.00 

1.67 

103.0 

0.032 

0.60 

0.47 

Total  conductor  length,  29,050  cm. 

Total  conductor  length,  29,050  cm. 

Spacing,  488  cm. 

Spacing,  366  cm. 

No.  8  new  H.  D.  copper  wire,  diam. 

No.  8  new  H.  D.  copper  wire,  diam. 

0.328  cm. 

0.328  cm. 
Temperature,  wet,  1.5  deg.  C. 

Temperature,   wet,  —  1.5  deg.  C. 
dry,  +  1-5  deg.  C. 

dry,  1.5  deg.  C. 

Barometer,  75.5  cm. 

Barometer,  76.6  cm. 

Bright  sun,  slight  breeze. 

Bright  sun,  slight  breeze. 

DATA  APPENDIX 


255 


Test  No.  92,  Line  B 

Test  No.  95,  Line  B 

Kv.  bet. 
lines 

Amp. 

Kw. 

Kw.  line 
loss,  p 

Kv.  bet. 
lines 

Amp. 

K\7. 

Kw.  line 
loss,  p 

27.5 

0.008 

222.0 

0.115 

8.80 

7.00 

34.5 

0.009 

199.8 

0.104 

6.80 

5.38 

39.5 

0.011 

181.0 

0.089 

5.36 

4.24 

44.5 

0.013 

0.02 

0.01 

158.0 

0.076 

3.80 

2.98 

51.0 

0.015 

0.05 

0.04 

140.0 

0.064 

2.84 

2.24 

56.5 

0.017 

0.10 

0.09 

120.0 

0.053 

1.92 

1.44 

61.5 

0.019 

0.22 

0.20 

102.0 



1.21 

0.96 

66.5 

0.023 

0.37 

0.31 

91.5 

0.034 

0.93 

0.75 

71.0 

0.024 

0.49 

0.40 

79.5 

0.028 

0.63 

0.51 

76.0 

0.028 

0.60 

0.49 

68.7 

0.021 

0.63 

0.52 

83.0 

0.032 

0.81 

0.66 

60.0 

0.017 

0.18 

0.16 

90.5 

0.037 

1.07 

0.88 

50.0 

0.014 

101.0 

0.041 

1.43 

1.17 

Total  conductor  length,  29,050  cm. 

110.5 

0.050 

1.80 

1.46 

Spacing,  550  cm. 

120.5 

0.055 

2.30 

1.88 

0.066    in.    galv.    steel   wire,    diam. 

131.5 

0.060 

2.80 

2.28 

168  cm. 

Temperature,    wet,  1.0  deg.  C. 

144.5 

0.068 

3.50 

2.84 

dry,  3.0  deg.  C. 

158.0 

0.081 

4.40 

3.57 

Barometer,  75.0  cm. 

170.0 

0.086 

5.30 

4.33 

Cloudy,  no  wind. 

181.0 

0.094 

6.18 

*    5.15 

190.0 

0.099 

6.70 

5.43 

204.0 

0.110 

8.00 

6.50 

215.0 

0.117 

9.00 

7.30 

222.0 

0.123 

9.64 

7.84 

Total  conductor  length,  29,050  cm. 

Spacing,  410cm. 

0.066-in.   galv.  steel   wire,  diam.   168 

cm. 

Temperature,  wet,  0.5  deg.  C. 
dry,  2.0  deg.  C. 
Barometer,  75.0 
Cloudy,  no  wind. 


256 


DIELECTRIC  PHENOMENA 
TRANSFORMER  Loss 


Kv. 

Amperes 

Kw. 

Kv. 

Amperes 

Kw. 

101.5 

0.008 

71.5 

0.005 

0.02 

131.5 

0.010, 

0.15 

82.0 

0.006 

0.03 

147.3 

0.011 

0.25 

97.0 

0.007 

0.05 

112.0 

0.008 

0.06 

163.8 

0.013 

0.42 

132.8 

0.009 

0.09 

181.5 

0.014 

0.54 

201.8 

0.016 

0.69 

149.0 

0.010 

0.12 

178.4 

0.013 

0.18 

30°  C. 

201.0 

0.014 

0.22 

223.0 

0.016 

0.30 

3°C. 

2.  D.C.  TESTS 
(Tests  from  Peek,  A.I.E.E.,  June,  1916,  unless  otherwise  noted) 

Spark-over  and  Corona  in  Air 

Sphere  Gaps. — The  d.c.  voltage  required  to  spark-over  a  given  spacing 
is  the  same  as  the  maximum  a.c. 

TABLE  I. — A.c.  AND  D.c.  SPARK-OVER  VOLTAGES  OF  2/0  NEEDLES  IN  AIR 


Spacing,  cm. 

Kilovolts 
60  cycle  (max.) 

Kilovolts 
d.c. 

5.1 

51.0 

52.0 

7.6 

62.5 

63.0 

10.2 

76.5 

73.5 

12.7 

88.3 

82.5 

15.3 

98.3 

90.5 

5  =  0.98 


Hum.  =  34  per  cent. 


TABLE  II. — D.c.  AND  A.c.  VISUAL  CORONA  AND  SPARK-OVER  VOLTAGES 
(Concentric  Cylinders — Normal  Air  Density  5=1) 


R 

Corona 

Spark-over 

outer 
cylinder, 

wire 
radius, 

R/r 

60  cycle 
calc. 

D.c. 

+ 

D.c. 

A.c. 

Ovmax 

D.c. 
fe 

60  cy. 

kv. 

D.c. 

+ 

D.c. 

cm. 

(max.) 

kv. 

kv. 

kv./cm. 

kv./cm. 

max. 

kv.' 

kv. 

3.81 

0.0038 

1000.0 

4.9 

6.4 

6.4 

186.0 

244.0 

Vibrates  be- 

3.81 

0.0129 

295.0 

8.4 

8.4 

8.3 

113.0 

113.0 

70.0 

fore  sparkover 

3.81 

0.0573 

66.5 

17.2 

17.2 

17.2 

71.5 

71.5 

40.0 

52.8 

61.0 

3.81 

0.130 

29.3 

25.2 

25.2 

25.2 

56.9 

56.9 

25.5 

,48.8 

54.5 

3.81 

0.239 

16.0 

33.5 

33.8 

33.8 

51.0 

51.3 

33.9 

47.5 

52.8 

3.81 

0.635 

6.0 

48.9 

49.0 

49.0 

42.9 

43.0 

48.1 

49.5 

53.2 

3.81 

1.110 

3.4 

54.7 

54.8 

54.8 

40.5 

40.6 

54.5 

54.5 

55.5 

DATA  APPENDIX 


257 


TABLE  111. — D.c.  AND  A.c.  VISUAL  CORONA  VOLTAGES 

(Concentric  Cylinders  at  Various  Air  Densities) 


A    p 

R 
radius 
outer 

r 
radius 

R/r 

5 

A.C. 

calc. 
60  cy. 

D.c. 

+ 

D.c. 

A.c. 
calc. 

D.c. 

Ov 

+      ' 

D.c. 

gv 

cylinder 
cm. 

wire 
cm. 

kv. 
(max.) 

kv. 

kv. 

gv 

(max.) 

kv./cm. 

kv./cm. 

2.90 

0.239 

12.1 

1.00 

30.0 

30.0 

30.0 

50.5 

50.5 

50.5 

2.90 

0.239 

12.1 

0.915 

28.0 

27.8 

27.8 

47.0 

46.8 

46.8 

2.90 

0.239 

12.1 

0.857 

26.3 

26.2 

44.2 

.... 

44.0 

2.90 

0.239 

12.1 

0.824 

25.7 

25.5 

.... 

43.3 

42.9 

.... 

2.90 

0.239 

12.1 

0.797 

25.1 

.... 

25.1 

42.2 

.... 

42.2 

2.90 

0.239 

12.1 

0.720 

23.1 

23.1 

.... 

38.8 

38.8 

.... 

2.90 

0.239 

12.1 

0.680 

22.1 

.... 

22.1 

37.1 

37.1 

.... 

2.90 

0.239 

12.1 

0.550 

19.1 

19.2 

19.3 

32.1 

32.2 

32.4 

2.90 

0.239 

12.1 

0.435 

15.7 

15.7 

16.0 

26.4 

26.4 

26.9 

2.90 

0.239 

12.1 

0.357 

13.5 

13.5 

22.7 

22.7 

2.90 

0.239 

12.1 

0.260 

10.7 

10.9 

11.6 

18.0 

18.4 

19.5 

2.90 

0.239 

12.1 

0.082 

4.8 

4.4 

4.6 

8.07 

7.4 

7.75 

TABLE  IV. — COMPARISON  OF  RESULTS* 
Critical  Surface  Intensity:  Kilo  volts  per  Centimeter 


Alternating  current 

Continuous  current 

Diam. 
wire, 

White- 
head 

Peek 

White- 
head  & 

White- 
head  & 
Brown 

Farwell 

White- 
head  & 
Brown 

Farwell 

cm. 

Brown 

0.074 

81.2 

80.7 

80.3 

76.0 

75.7 

80.8 

76.9 

0.090 

76.6 

76.0 

76.0 

71.9 

71.6 

76.1 

72.0 

0.107 

72.9 

72.3 

72.5 

68.9 

68.3 

72.4 

69.8 

0.125 

69.9 

69.2 

69.6 

66.2 

65.5 

69.3 

67.2 

0.166 

64.8 

64.1 

64.8 

61.9 

61.1 

64.2 

62.9 

0.231 

59.9 

59.1 

60.1 

57.6 

56.6 

59.1 

58.7 

1Whitehead,  A.I.E.E.,  Feb.,  1917.     See  also  Whitehead,  A.I.E.E.,  June, 
1920. 

TABLE  V. — SURFACE  SPARK-OVER  OF  SUSPENSION  INSULATORS 


D  c   kv 

Insulator 

60  cycle 

number 

kv.  (max.) 

cap  + 

cap  — 

1 

116.0 

117.5 

127.5 

2 

99.0 

99.0 

106.0 

3 

126.0 

132.0 

139.0 

4 

111.5 

128.0 

135.0 

5 

119.0 

128.0 

135.0 

258 


DIELECTRIC  PHENOMENA 


D.c.  Spark-over  in  Oil 

TABLE  VI. — D.c.  AND  A.c.  SPARK-OVER  TESTS  ON  2/0  NEEDLES  IN  No.  8 
TRANSIL  OIL  AT  25  DEG.  C. 


Needle  gap, 
cm. 

60  cycle 
kv.  (max.) 

D.c. 
kv.  (max.) 

0.317 

21.2 

21.7 

0.635 

34.7 

33.5 

1.27 

50.5 

50.2 

1.91 

65.0 

66.0 

2.54 

86.5 

82.5 

D.c.  Strength  of  Solid  Insulation 
TABLE  VII. — VARIATION  OF  60  CYCLE  PUNCTURE  VOLTAGE  WITH  TIME  OF 

APPLICATION  ON  VARNISHED  CAMBRIC 
Tests  Between  2.5-in.  Plates,  1%-m.  Radius  Edge,  in  No.  6  Transil  Oil 


Temperature, 
deg.  C. 

Sheets 

Thickness, 
mm. 

kv. 
(max.) 

Time, 
sec. 

•25 

1 

0.30 

24.8 

2.3 

(12  mils) 

21.3 

12.0 

19.5 

17.3 

17.7 

41.5 

15.9 

198.0 

14.2 

900.0 

100 

1 

0.30 

14.5 

2.0 

13.2 

7.0 

12.6 

11.0 

12.0 

25.0 

10.8 

620.0 

9.9 

1400.0 

25 

2 

0.60 

29.8 

213.0 

26.7 

700.0 

25.6 

1418.0 

25 

3 

0.90 

53.0 

8.0 

45.2 

51.5 

42.5' 

80.0 

41.7 

138.0 

38.9 

370.0 

37.1 

905.0 

25 

4 

1.20 

69.3 

4.0 

65.0 

13.0 

64.3 

15.0 

55.8 

39.0 

53.0 

80.0 

50.8 

155.0 

47.3 

580.  OJ 

DATA  APPENDIX 


259 


TABLE   VIII. — VARIATION   OF  D.c.    PUNCTURE   VOLTAGE   WITH  TIME  OP 

APPLICATION  ON  VARNISHED  CAMBRIC 
Tests  Between  2.5-in.  Plates,  l>£-in.  Radius  Edge,  in  No.  6  Transil  Oil 


Temperature, 
deg.  C. 

Sheet 

Thickness, 
mm. 

kv. 
(max.) 

Time, 
sec. 

25 

1 

0.30 

28.  S 

8.3 

27.2 

20.0 

25.5 

54.0 

23.8 

94.0 

22.1 

363.0 

20.4 

668.0 

18.8 

5400.0 

100 

1 

0.30 

21.0 

1.5 

20.3 

2.0 

19.6 

38.0 

18.6 

72.0 

17.0 

600.0 

15.9 

470.0 

15.2 

1920.0 

25 

2 

0.60 

52.5 

26.0 

50.0 

50.0 

47.0 

230.0 

25 

3 

0.90 

80.3 

68.0 

77.5 

130.0 

77.2 

350.0 

75.5 

1400.0 

25 

4 

1.20 

127.2 

7.0 

120.0 

16.0 

115.2 

45.0 

110.0 

100.0 

107.5 

185.0 

105.0 

330.0 

104.6 

730.0 

260 


DIELECTRIC  PHENOMENA 


TABLE  IX. — A.c.  AND  D.c.  PUNCTURE  VOLTAGES  OF  VARNISHED  CAMBRIC 
FOR  VARIOUS  THICKNESSES  AND  TIME  OF  APPLICATION 


Time  of  application,  seconds 


100 


50 


10 


Sheets 

Thickness, 
mm. 

Kilovolts  to  puncture 
(max.) 

1 

0.30  a.c. 
0.30d.c. 

11.0 
18.0 

16.5 
23.5 

17.5 
24.5 

20.5 
27.5 

25.5 
32.5 

2 

0.60  a.c. 
0.60  d.c. 

20.0 
43.0 

31.0 
49.5 

33.0 
51.0 

39.0 
55.5 

47.0 
62.5 

3 

0.90  a.c. 
0.90d.c. 

30.0 
70.0 

42.0 
79.0 

45.0 
81.0 

52.0 
86.0 

62.0 
95.0 

4 

1.20  a.c. 
1.20d.c. 

37.0 
96.0 

52.0 
111.0 

55.0 
114.0 

64.0 
123.0 

78.0 
137.0 

Gradient  Kv.  per  Mm.  (Max.) 


1 

0  .  30  a.c. 
0  .  30  d.c. 

36.6 
60.0 

55.0 
75.0 

58.5 
82.0 

68.5 
92.0 

85.0 
108.0 

2 

0.60a.c. 
0.60d.c. 

33.3 
72.0 

51.5 
82.0 

55.0 
85.0 

65.0 
92.0 

78.0 
104.0 

3 

0.90  a.c. 
0  .  90  d.c. 

33.3 
77.5 

46.5 

87.5 

50.0 
90.0 

57.9 
95.5 

69.0 
105.0 

4 

1.20  a.c. 
1.20  d.c. 

30.9 
80.0 

43.3 
92.5 

45.8 
95.0 

53.2 
102.0 

65.0 
106.0 

DATA  APPENDIX 


261 


3.  STRENGTH  OF  AIR  FILMS 

CORONA  TESTS  ON  AIR  FILMS  BETWEEN  Two  GLASS  PLATES 
(60  ~. — Glass  Plate  on  Each  Electrode) 


Thickness, 
cm. 

Per- 
mittivity 

> 

starting 
voltage 
maxi- 
mum 

Strength  of 
air  films 
kv./cm.  max. 
reduced  to  6  =  1 

Temp, 
deg.  C. 
t 

Bar 
pressure 
b 

\ir 

Both 

glass 

cm. 

space 

plates 

Ea 

go. 

Os 

0.0025 

0.910 

7.2 

0.96 

21,100 

161.0 

196.0 

285 

73.6 

0.0053 

0.910 

7.2 

0.96 

17,400 

137.0 

139.0 

285 

73.6 

0.0120 

0.910 

7.2 

0.96 

10,600 

88.0 

95.0 

285 

73.6 

0.028 

0.910 

7.2 

0.96 

9,350 

63.0 

59.0 

285 

73.6 

0.0562 

0.910 

7.2 

0.96 

9,050 

53.0 

50.6 

285 

73.6 

0.122 

0.910 

7.2 

0.96 

10,700 

44.5 

44.5 

285 

73.6 

0.275 

0.910 

7.2 

0.96 

14,300 

36.8 

39.3 

285 

73.6 

0.455 

0.910 

7.2 

0.96 

19,100 

35.6 

36.8 

285 

73.6 

0.0051 

0.910 

9.3 

0.74 

7,660 

101.0 

143.0 

114 

72.9 

0.0122 

0.910 

9.3 

0.74 

7,050 

96.5 

95.0 

114 

72.9 

0.0260 

0.910 

9.5 

0.73 

5,180 

58.5 

59.6 

120 

72.9 

0.0560 

0.900 

9.4 

0.73 

5,890 

53.0 

50.6 

116 

72.5 

0.120 

0.900 

9.4 

0.73 

6,670 

42.4 

44.4 

117 

0.275 

0.900 

9.3 

0.73 

10,100 

37.3 

.39.0 

114 

72.5 

0.455 

0.900 

9.3 

0.73 

14,160 

35.1 

36.8 

116 

72.5 

Corona  on  Air  Films  Between  Tape  Insulated  Conductors 

0.635 
0.630 

0.645 
0.645 

3.2 
3.5 

0.95 
0.75 

26,900 
33,400 

34.0 
36.2 

35.1 
35.1 

25 
107 

72.8 
72.8 

ga  =  strength  of  entrapped  film. 
Os  •=  strength  of  film  between  metal  spheres. 

See  Dubsky,  Dielectric  Strength  of  Air  Films  Entrapped  in  Solid  Insulation,  A.I.E.E. 
Feb.,  1914. 


262 


DIELECTRIC  PHENOMENA 


SPARK-OVER  OF  GAPS  AT  SMALL  SPACINGS  AND  VARIOUS  AIR  DENSITIES 


Spark-over,  volts 
(Max.) 

px 

dx 

0.010 

0.000132 

1050 

0.015 

0.000197 

640 

0.020 

0.000264 

400 

0.030 

0.000394 

355 

0.040 

0.000526 

350 

0.050 

0.000660 

395 

0.100 

0.001320 

550 

0.300 

0.003950 

700 

0.500 

0.00660 

850 

0.700 

0.00920 

1030 

0.965 

0.01270 

1700 

1.930 

0.02540 

2200 

2.900 

0.03820 

2700 

3.860 

0.05100 

3750 

5.800 

0.07650 

4680 

7.740 

0.1020 

5600 

9.660 

0.1270 

6530 

11.600 

0.1520 

7370 

13.520 

0.1770 

8210 

15.450 

0.2010 

x  =  spacing,  cm. 
p  =  pressure,  cm. 
8  =  relative  air  density. 

Paschen's  Law:  To  find  spark-over  voltage  multiply  pressure  or  density 
by  spacing  and  find  corresponding  Emax. 


DATA  APPENDIX 


263 


4.  THE  EFFECT  OF  TRANSIENT,  IMPULSE,  OR  LIGHTNING  VOLT- 
AGES ON  AIR,  OIL  AND  SOLID  INSULATION 

The  following  tests  were  made  by  means  of  the  impulse  generator  shown 
in  Fig.  147  (a).  Unless  otherwise  noted  the  impulses  correspond  to  single 
half  cycles  of  sine  waves  of  the  indicated  frequency.  The  time'of  application 
is,  therefore,  generally  not  more  than  a  few  microseconds1  (millionths  of  a 
second). 

Wave  Shape 

TABLE  1. — IMPULSE  SPARK-OVER  VOLTAGES  OP  NEEDLES  AND  SPHERES 
(Effect  of  Wave  Shape) 


Needle  gap 

Sphere  gap 
(25  cm.  spheres) 

Contin- 

Contin- 

uously 

Impulse 

uously 

Impulse 

Spacing,  cm. 

applied 
(60  ~) 
spark- 

spark- 
over 
kv. 

Imp. 
ratio 

Spacing, 
cm. 

applied 
(60  ~) 
spark- 

spark- 
over 
kv. 

Imp. 
ratio 

over  kv. 

(max.) 

over  kv. 

(max.) 

(max.) 

(max.) 

Wave  No.  1  (Sine  Shape) 

2.30 

26.5 

36.5 

1.34 

1.15 

35.5 

35.5 

1.00 

3.50 

38.0 

60.0 

1.58 

2.00 

59.0 

60.0 

1.02 

4.50 

45.0 

77.2 

1.71 

2.60 

75.0 

77.2 

1.03 

5.10 

49.1 

91.0 

1.86 

3.00 

87.0 

90.0 

1.05 

5.40 

51.2 

102.0 

1.99 

6.10 

56.2 

113.0 

2.00 

6.70 

59.0 

119.0 

2.02 

R  =  520  ohms                                       C  =  0.0005  X  10-6  farads 

L  =  0.312  X  10-3  henrys 
Wave  No.  4 


8.80 

70.5 

81.5 

.16 

2.60 

80.0 

81.5 

1.02 

12.50 

87.5 

105.0 

.20 

3.50 

103.0 

105.0 

1.02 

21.00 

127.0 

145.0 

.14 

5.40 

145.0 

145.0 

1.00 

23.80 

141.0 

163.0 

.16 

6.50 

159.0 

163.0 

1.02 

26.40 

152.0 

180.0 

.18 

30.50 

171.0 

207.0 

.21 

R  =  6800                                                  C  =  0.004  X  10-6  farads 

L  =  0.604  X  10~3  henrys 


0.2 

75 


0.5 
100 


1.0 

48 


1.5 
-10 


4.0 
0 


Wave  No.  1 
Time,  microseconds  ..............   00     0.1 

Per  cent.  max.  kv  .................     0         52 

Wave  No.  4 
Time,  microseconds  ..............   0.0     0.1 

Per  cent.  max.  kv  ................     0         52 

Wave  No.  1  approximately  half  cycle  sine  wave. 
R,  L  and  C  constants  of  impulse  circuit. 

1  Peek,    The    Effect    of    Transient    Voltages    on    Dielectrics,    A.I.E.E. 
Transactions,  1915,  page  1857. 


264 


DIELECTRIC  PHENOMENA 


Time  Lag — Frequency 

TABLE  II. — VARIATION  OF  SPARK-OVER  VOLTAGES  OF  SPHERES  AND  NEEDLES 
FOR  SINGLE  HALF  CYCLES  OF  SINE  WAVES  CORRESPONDING  TO 
DIFFERENT  FREQUENCIES     . 


Needles 

Spheres  25  cm. 

60  ~ 

Impulse 

60  ~ 

Impulse 

Spacing, 

spark- 

spark- 

Impulse 

Spacing, 

spark- 

spark- 

Impulse 

cm. 

over 

over 

ratio 

cm. 

over 

over 

ratio 

kv.  (max.) 

kv.  (max.) 

kv.  (max.) 

(max.) 

R  =  2080  ohms 


55  Kilocycles 


3.50 

38.0 

38.0 

1.00 

1.25 

38.0 

38.0 

1.00 

5.10 

49.4 

49.4 

.00 

1.65 

49.4 

49.4 

1.00 

7.00 

59.2 

59.2 

.00 

2.00 

59.2 

59.2 

1.00 

8.50 

69.0 

69.0 

.00 

2.35 

69.0 

69.0 

1.00 

9.60 

75.0 

76.0 

.01 

2.60 

76.0 

76.0 

1.00 

10.60 

79.0 

84.0 

.06 

2.90 

83.5 

84.0 

1.00 

11.30 

83.0 

91.0 

1.09 

3.10 

90.5 

91.0 

1.00 

12.50 

88.5 

97.0 

1.10 

3.40 

97.5 

97.0 

1.00 

13.70 

94.5 

106.0 

1.12 

3.70 

104.0 

106.0 

1.02 

R  =  700  ohms                          L  =  3.17  X  10-8  henrys                          C  -  0.004  X  10-6  farads 

100  Kilocycles 

2.70 

31.8 

35.4 

.10 

....                .... 

6.50 

58.0 

65.0 

.13 

....                .... 

9.0 

71.5 

89.0 

.26 

.... 

11.4 

83.5 

110.0 

.32 

13.6 

93.0 

127.0 

.36 

L  -  2.50  X  10-3  henrys 


C  =  0.001  X  10-«  farads 


350  Kilocycles                     12.5  cm.  Spheres 

2.20 

26.1 

32.6 

1.25 

1.05 

33.0 

32.6 

0.99 

3.20 

35.2 

50.2 

1.42 

1.65 

49.4 

50.2 

1.02 

4.30 

44.4 

67.0 

1.51 

2.30 

65.6 

67.0 

1.02 

5.85 

55.0 

83.5 

1.52 

2.90 

81.0 

83.5 

1.03 

7.00 

61.2 

100.0 

1.63 

3.45 

95.0 

100.0 

1.05 

8.60 

69.5 

117.0 

1.68 

4.25 

113.0 

117.0 

1.05 

9.85 

76.0 

134.0 

1.76 





R  -  430  ohms                         L  -  0.312  X  10-s  henrya                         C  =  0.001  X  10-«  farads 

900  Kilocycles 

1.65 

9.2 

14.2 

1.52 

0.40 

14.1 

14.1 

1.00 

1.20 

15.2 

28.3 

•     1.86 

0.90 

28.2 

28.2 

1.00 

1.80 

21.6 

42.3 

1.91 

1.40 

42.3 

42.3 

1.00 

2.60 

29.7 

56.5 

1.92 

1.90 

55.0 

56.5 

1.02 

3.10 

33.9 

70.7 

2.08 

2.40 

68.0 

70.5 

1.03 

3.60 

38.9 

84.7 

2.18 

2.90 

82.0 

84.5 

1.03 

4.OO 

42.3 

99.0 

2.34 

3.50 

95.0 

98.5 

1.04 

.... 

3.70 

100.0 

106.0 

1.06 

R  •=  400  ohms                        L  =  0.166  X  10-"  henrys                        C  =  0.00025  X  10-"  farads 

The  above  waves  are  single  half  cycles  of  sine  waves  of  the  frequency  indicated. 


DATA  APPENDIX 


265 


Bar  =  76  cm. 


Corona 

TABLE  III. — TRANSIENT  CORONA 
(Single  Half  Sine  Wave) 

Concentric  Cylinders  in  Air 
t  =  25  deg.  C.  5  =  1  Outer  Cyl.  rad.  R 


8.8  cm. 


Wire 
radius 
r 
cm. 

60  ~  tests 

Impulse  tests 

Calc. 
corona 
kv.  (max.) 

Test 
corona 
kv.  (max.) 

Test 
spark- 
over 
kv.  (max.) 

Corona 

Spark- 
over 
kv. 
(max.) 
1  in  10 

Single  half 
sine  wave 
frequency 
kilocycles 

A 
kv.  (max.) 

B 

kv.  (max.) 

0.0318 
0.0573 
0.130 
0.95 
1.425 

13.4 
20.0 
31.3 
85.0 
98.0 

135.0 
110.0 
49.6 
86.0 
98.0 

13.8 
14.7 
15.1 

21.2 
22.0 
22.6 

32.3 
33.5 
34.2 

85.0 
87.0 
87.5 

99.0 
99.0 
100.0 

15.6 
16.0 
16.1 

23.7 
24.0 
24.0 

33.2 
34.0 
34.8 

86.0 
87.5 
88.0 

99.0 
99.5 
101.0 

100.0 

100 
500 
900 

100 
500 
900 

100 
500 
900 

100 
500 
900 

100 
500 
900 

20.5 
31.4 
86.0 
100.0 

100.0 

103.0 

108.0 
110.0 

Bar  =  76  cm. 


t  =  25  deg.  C. 


5=1 


3.81  cm. 


0.0129 

5.7 



8.5 
9.2 
9.5 

'.'.'.'. 

32.0 
68.0 

100 
500 
900 

0.0318 

12.3 

12.0 

49.0 

13.4 
13.5 
14.5 

14.7 
14.7 
15.0 

33.0 
67.5 

100 
500 
900 

0.0573 

17.2 

.... 

40.0 

17.4 
20.0 
24.0 

18.2 
20.5 
24.7 

35.0 
66.0 

100 
500 
900 

0.239 

33.5 



33.9 

33.4 
37.0 

37.1 

38.9 
37.0 

44.7 
63.7 
103.0 

100 
500* 
900 

0.318 

38.0 

37.9 

37.9 

38.5 
39.5 
41.6 

39.0 
40.0 
42.0 

45.0 
64.0 
98.0 

100 
500 
900 

0.635 

49.0 

48.1 

48.1 

49.0 
50.0 
51.6 

49.7 
50.5 
52.0 

50.0 
62.0 
81.0 

100 
500 
900 

1.27 

55.0 

55.0 

54.5 

55.0 
56.0 
56.0 

55.0 
56.0 
56.0 

55.0 
57.0 
59.3 

100 
500 
900 

Comparison  of  60  ~  and  transient  corona  for  different  sizes  of  wire  in  center  of  a  cylinder. 
The  voltage  at  which  transient  corona  first  appeared  is  given  in  col.  A.  Corona  appeared 
on  every  application  for  voltages  given  in  col.  B.  The  difference  is  probably  for  positive 
and  negative  wire. 


266 


DIELECTRIC  PHENOMENA 


Air  Density 

TABLE  IV. — EFFECT  OF  AIR  DENSITY  ON  TRANSIENT  CORONA  AND  SPARK- 
OVER 
Concentric  Cylinders1 

Outer  cylinder  radius,  R  =  3.08.     Inner  cylinder,  r  =  0.0573  cm. 


Corona 


Meas. 
60~ 
kv. 
max. 

Cal. 
60  ~ 

kv. 

max. 

Impulse 
kv. 
max. 

Impulse 
ratio 

8 

60  ~ 
kv. 
max. 

Impulse 
kv. 
max. 

Impulse 
ratio 

5 

Single 
half 
sine 
freq. 
kilo- 
cycles 

2.8 

2.75 

3.5 

1.27 

0.064 

10.7 

0.064 

100 

4.8 

4.80 

5.5 

1.15 

0.160 

7.0 

13.0 

'1.86 

0.160 

100 

6.0 

5.95 

6.65 

1.13 

0.248 

9.3 

15.5 

1.67 

0.248 

100 

7.6 

7.57 

8.4 

1.10 

0.330 

11.0 

17.5 

1.59 

0.330 

100 

11.6 

11.60 

12.7 

1.09 

0.630 

16.6 

27.3 

1.65 

0.630 

100 

14.4 

14.40 

15.5 

1.07 

0.847 

20.2 

30.2 

1.50 

0.847 

100 

16.2 

16.20 

17.2 

1.06 

1.00 

22.5 

31.9 

1.42 

1.000 

100 

2.6 

2.58 

4.0 

1.55 

0.051 

28.5 

0.040 

900 

4.8 

4.86 

6.5 

1.34 

0.166 

5.0 

31.0 

6.2 

0.085 

900 

7.6 

7.60 

10.1 

1.32 

0.333 

7.5 

37.0 

4.94 

0.173 

900 

9.5 

9.50 

12.1 

1.28 

0.465 

13.3 

47.0 

3.54 

0.440 

900 

13.5 

13.30 

16.3 

1.23 

0.765 

15.8 

53.0 

3.35 

0.590 

900 

16.2 

16.20 

20.0 

1.23 

1.00 

18.8 

60.0 

3.19 

0.765 

900 

22   5 

fi7   5 

a  on 

1  nn 

900 

Outer  Cylinder  Radius,  R  =  3.08  cm.     Inner  Cylinder,      =  0.635  cm. 

7.3 

7.7 

8.5 

1.16 

0.127 

7.3 

8.5 

.16 

0.127 

100 

13.0 

13.0 

14.9 

1.14 

0.253 

13.0 

14.9 

.14 

0.253 

100 

15.0 

15.3 

16.6 

1.11 

0.309 

15.0 

16.6 

.11 

0.309 

100 

17.0 

16.8 

18.3 

1.08 

0.350 

17.0 

18.3 

.08 

0.350 

100 

24.0 

23.8 

24.5 

1.02 

0.535 

24.0 

24.5 

.02 

0.535 

100 

29.0 

29.0 

28.9 

1.00 

0.702 

29.0 

28.9 

.00 

0.702 

100 

34.5 

35.5 

34.5 

1.00 

0.863 

34.5 

34.5 

.00 

0.863 

100 

39.0 

40.3 

40.5 

1.03 

1.002 

39.0 

40.5 

.03 

1.002 

100 

Outer  Cylinder  Radius,  R  =  3.08  cm.     Inner  Cylinder,  r  =  0.635  cm. 

3.5 

3.9 

8.6 

2.46 

0.049 

3.5 

20.3 

5.80 

0.049 

900 

9.0 

9.8 

11.9 

1.31 

0.165 

9.0 

25.0 

2.78 

0.165 

900 

14.0 

14.1 

17.3 

1.23 

0.280 

14.0 

30.5 

2.18 

0.280 

900 

21.2 

21.2 

22.5 

1.07 

0.462 

21.3 

37.6 

1.77 

0.462 

900 

26.2 

26.3 

28.0 

1.06 

0.604 

26.0 

43.5 

1.67 

0.604 

900 

32.0 

32.2 

35.6 

1.01 

0.773 

32.0 

48.5 

1.52 

0.773 

900 

39.0 

40.3 

40.2 

1.00 

1.00 

39.0 

52.5 

1.34 

1.00 

900 

Spark-over 


Tests  above  made  in  a  metal  lined  glass  tube. 


DATA  APPENDIX 


267 


Polarity 
TABLE  V. — POSITIVE  AND  NEGATIVE  SPARK-OVER 

(Dissimilar  Electrodes) 
Wire  in  Cylinder  R  =  3.81  cm. 


Voltage  kv. 

Radius, 

Per  cent. 

cm. 

wire 

difference 

+ 

- 

1.27 

57.0 

57.0 

0 

0.187 

51.0 

58.5 

15 

0.0318 

49.8 

60.6 

22 

Point  and  plate 


Spacing  cm.  for  a  given  applied  voltage  when  point  is 


5.15 


3.05 


Approx. — 500  kilocycle  wave. 

Air  Films 

TABLE  VI. — TRANSIENT  SPARK-OVER  VOLTAGES  AT  SMALL  SPACINGS 
(Between  6.25  cm.  Diameter  Spheres.     5  =  1) 


60  ~ 

100  kc.  impulse 

900  kc.  impulse 

Spark-over 

Spacing, 

Gradi- 

Gradi- 

Gradi- 

cm. 

Volts 

ent 

Volts 

ent 

Impulse 

Volts 

ent 

Impulse 

kv. 

kv.  per 

ratio 

kv. 

kv.  per 

ratio 

max. 

max. 

kv. 

kv.  per 

cm. 

cm. 

cm. 

0.0025 

0.50 

196 

0.78 

305.0 

1.57 

0.81 

325.0 

1.64 

0.0051 

0.73 

143 

1.23 

242.0 

1.69 

1.10 

216.0 

1.51 

0.0076 

0.90 

118 

1.70 

212.0 

1.80 

1.78 

235.0 

1.98 

0.0102 

1.07 

105 

2.11 

207.0 

1.98 

2.18 

215.0 

2.04 

0.0127 

1.17 

92 

2.44 

192.0 

2.08 

2.55 

200.0 

2.18 

0.025 

1.52 

60 

4.50 

178.0 

2.95 

5.00 

198.0 

3.04 

0.051 

2.62 

52 

6.15 

122.0 

2.35 

8.50 

168.0 

3.25 

0.102 

4.62 

46 

8.75 

87.0 

1.90 

12.80 

126.0 

2.77 

0.25 

9.77 

40 

14.90 

61.0 

1.52 

21.50 

84.1 

2.20 

0.51 

17.50 

36 

22.50 

46.0 

1.28 

28.50 

56.0 

1.63 

1.27 

39.20 

35 

42.00 

37.0 

1.06 

47.00 

37.0 

1.20 

1.90 

57.50 

35 

57.50 

35.0 

1.00 

62.50 

36.0 

1.09 

2.54 

88.50 

35 

88.50 

35.0 

1.00 

90.00 

35.0 

1.02 

Accuracy  of  impulse  voltages  best  above  5  kv. 


268 


DIELECTRIC  PHENOMENA 


Insulators 

TABLE  VII. — EFFECT  OF  POLARITY  ON  INSULATOR  SPARK-OVERS 

200  kc. 


60  ~  spark- 
over  kv.,  max. 

Impulse  spark-over  kv.  varying 
polarity,  max. 

Impulse  spark-over  kv. 
predetermined  polarity, 
max. 

Cap  + 

Cap  - 

98 

1    spark-over   in    10 
impulses. 

108 

108 

10  spark-overs  in  10 
impulses. 

130 

... 

134 

TABLE  VIII. — IMPULSE  SPARK-OVER  OF  SUSPENSION  INSULATORS  WET  AND 

DRY 


Ins. 
No. 

Type 

60  ~  arc-over 

100  kc.  impulse 

500  kc.  impulse 

(max.) 

arc-over 

arc-over 

Dry 

Wet 

Dry 

Wet 

Dry 

Wet 

A 

Two  piece  suspen- 
sion with  petti- 
coats. 

112 

72 

118 

114 

165 

162 

B 

Two  piece  suspen- 
sion with  petti- 
coats. 

116 

70 

128 

125 

172 

168 

.DATA  APPENDIX 


269 


TABLE    IX. — SPARK-OVER   VOLTAGE    OP   INSULATOR    AT    DIFFERENT    AIR 
PRESSURES  DURING  RAIN 

(See  Fig.  96) 
Rain  Tests  (0.2  in.  per  Minute  at  45  deg.) 


Room 
bar. 
cm. 

Vacuum 
cm. 
(in  the 

cask) 

Pressure 
cm. 
(in  the 
cask) 

Temp. 
C. 

(in  the 
cask) 

S 
(in  the 
cask) 

Kilo  volts 
spark-over 
(effective) 

60-cycle  Spark-over 


75.6 

41.2 

34.4 

18.0 

0.46 

28 

75.6 

36.0 

39.6 

18.0 

0.53 

31 

75.6 

31.1 

45.5 

18.0    • 

0.61 

35 

75.6 

25.0 

«    50.6 

18.0 

0.68 

39 

75.6 

15.6 

59.0 

18.0 

0.79 

45 

75.6 

7.8 

67.8 

18.0 

0.91 

50 

75.6 

0.0 

75.6 

18.0 

1.02 

57 

Impulse  Spark-over  200  Kilo  Cycles— Single  Wave  (Effective  Kv.) 


75.6 

41.2 

34.4 

18.0 

0.46 

62 

75.6 

36.0 

39.6 

18.0 

0.53 

68 

75.6 

31.1 

45.5 

18.0 

0.61 

72 

75.6 

25.0 

50.6 

18.0 

0.68 

77 

75.6 

15.6 

59.0 

18.0 

0.79 

84 

75.6 

7.8 

67.8 

18.0 

0.91 

92 

75.6 

0.0 

75.6 

18.0 

1.02 

98      • 

F.  W.  Peek,  Jr.,  "  The  Effect  of  Altitude  on  the  Spark-over  Voltage  of 
Bushings,  Leads  and  Insulators."     A.I.E.E.,  Dec.,  1914. 

G.  E.  Review,  June,  1916.    Tests  made  in  a  large  wooden  cask. 


270 


DIELECTRIC  PHENOMENA 


Oil 

TABLE  X. — IMPULSE  AND  60  ~  BREAK-DOWN  VOLTAGES  IN  OIL 


Spacing, 
cm. 

60  ~ 
kv.  max. 

Impulse 
kv.  max. 

Impulse 
ratio  oil 

Impulse  ratio 
same  spacing 
in  air 

/ 

0.5 


Between  Disks  2.5  cm.  Diameter 


56.6 


170 


3.00 


Between  Needles 


2.54  Spheres — Small  Spacings 
Spacing  less  than  4  \/R 


Approx.  230 
kc. 


1.0 

50.0 

103 

2.00 

2.0 

69.0 

157 

2.20 

1.20 

Approx.  230 

kc. 

3.0 

89.0 

233 

2.60 

1.21 

4.0 

108.0 

321 

3.00 

1.25 

0.25 

70.0 

160 

2.30 

.... 

0.50 

100.0 

245 

2.45 



Approx.  230 
kc. 

0.70 

115.0 

270  ' 

2.35 

1.00 

140.0 

285 

2.05 

TABLE  X  (Continued'). — IMPULSE  AND  60  ~  BREAK-DOWN  VOLTAGES  IN  OIL 
Between  2/0  Needles 


Needle 
spacing,  cm. 

60  'v  spark- 
over  kv.  (max.) 

Impulse, 
kv. 

Impulse 
ratio 

/ 

0.32 

28.0 

36.5 

1.30 

100  kc. 

0.64 

40.0 

70.0 

1.75 

(single 

1.27 

63.0 

128.5 

2.04 

half  sine 

1.70 

74.0 

175.0 

2.37 

wave) 

2.00 

81.0 

3.00 

104.0 

0.20 

20.0 

36.0 

1.80 

500  kc. 

0.32 

28.0 

64.0 

2.30 

(single 

0.42 

31.5 

92.0 

2.92 

half  sine 

0.56 

37.0 

121.5 

3.29 

(wave) 

DATA  APPENDIX 


271 


TABLE  XI. — COMPARATIVE  STRENGTH  OF  OIL  FOR  HIGH  FREQUENCY,  IM- 
PULSE, OSCILLATORY,  AND  60  CYCLE  VOLTAGES 
(Transil  Oil  Between  Flat  Disk  Terminals,  Square  Edges.    2.5  cm.  Diameter; 

0.25  cm.  Space) 
Break-down  Gradients 


60  cycle  kv.  per  cm. 
max. 

Single  impulse  sine 
shape  corresponding 
to  200  kilocycles, 
kv.  per  cm.  max. 

Damped  oscillations 
train  frequency  120 
per  second.     Fre- 
quency 200  kilocycles, 
kv.  per  cm.  max. 

High-frequency  al- 
ternator 90  kilo- 
cycles, 
kv.  per  cm.  max. 

170 

390 

300 

67 

Solid  Insulations 

TABLE  XII. — COMPARATIVE  INSULATION  STRENGTH  FOR  HIGH  FREQUENCY, 

IMPULSE,  OSCILLATORY  AND  60  CYCLE  VOLTAGES 

Temperature  30  deg.  C. 


60  cycles 

High  frequency 
(alternator) 
90,000  cycles 

Damped  oscilla- 
tion.    Train 
freq.  120  sec. 
200,000  cycles 

Single  im- 

pulse sine 
shape,  cor- 
responding 
to  half 
cycle  of 

Imp. 
ratio 

Thick- 
ness, 
cm. 

Lay- 
ers 

200,000  cy. 

kv.  per  cm. 

kv.  per  cm. 

kv.  per  cm. 

kv.  per  cm. 

(max.) 

(max.) 

(max.) 

(max.) 

Rapidly 
applied 

1  min. 

Rapidly 
applied 

1  min. 

Rapidly 
applied 

1  min. 

Transil  Oil  Between  Flat  Terminals — Square  Edge 
2.5  cm.  Diameter — 0.25  cm.  Space 


170 

67 

300 

390 

2.10 

0.25 

1 

Oiled  Pressboard 

10  cm.  Diameter  Square  Edge  Disks  in  Oil 

355 

310 

95 

72.0 

370 

290 

720 

2.3 

0.25 

1 

395 

370 

61 

41.0 

420 

240 

0.50 

2 

25 

17.6 

1.50 

3 

Varnished  Cloth 
10  cm.  Diameter  Square  Edge  Disks  in  Oil 


530 

465 

195 

176.0 

1080 

2.26 

0.06 

2 

420 

310 

135 

100.0 

550 

560 

780 

2.50 

0.15 

5 

420 

310 

100 

73.0 

490 

410 

700 

2.25 

0.25 

8 

330 

275 

410 

305 

600 

2.20 

0.36 

12 

"Rapidly  applied"  voltage  brought  to  puncture  value  in  a  few  seconds. 


272  DIELECTRIC  PHENOMENA 

6.  STRENGTH  OF  OIL  AT  LARGE  SPACINGS 
BETWEEN  POINTS 

Spacing,  cm.  Spark-over,  k.v.  max. 

5  127 

10  226 

20  395 

30  510 

40  610 

50  662 

60  735 

70  805 

FLAT  Discs  WITH  ROUNDED  EDGE 

25  cm.  diameter  Radius  of  edges,  2.5  cm. 
5  310 

10  460 

15  650 

20  780 

25  900 

If  the  space  between  the  discs  is  divided  into  ducts  by  press- 
board  barriers,  the  total  breakdown  voltage  will  be  increased. 
Incipient  sparks  will,  however,  start  at  the  voltages  in  the 
table.  It  is  assumed  that  the  barriers  do  not  occupy  more  than 
25  per  cent,  of  the  space. 

The  above  tests  were  made  on  dry  oil  at  60  cycles. 


INDEX 

A 

PAGE 

Air,  at  very  low  pressures 196 

compressed 42 

density 51 

occluded  in  solid  insulation 236 

see  Corona. 
Altitude,  effect  of,  on  arc-over  of  bushings,  leads  and  insulators. .    Ill,  217 

effect  of,  on  corona 42,  50,  51 

effect  of,  on  corona  loss 146 

effect  of,  on  sphere-gap  spark-over 95 

variation  of  air  density  with 51 

B 

Barriers  in  oil • appendix,  155,  169,  189,  272 

Beta  particle 193 

Bushing,  condenser  type 220 

effect  of  altitude  on  spark-over  of .'  Ill 

oil-filled  type 220 

overstressed  air  in 217 

rod  and  torus 220 

transformer . .  220 


C 

Cable,  graded 33,  218 

Capacity,  see  Permittance. 

Cathode  rays 192 

Compressed  air 42 

Corona,  application  of  electron  theory  to 194 

at  very  low  air  density 196 

calculations  for  practical  transmission  lines 199 

condition  for  spark  or 27,  79,  84 

in  entrapped  air  films appendix,  61,  196,  236 

in  oil ' 155 

Corona  loss,  a.c.  and  d.c 132 

description  of  experimental  lines 117 

disruptive  critical  voltage 137 

273 


274  INDEX 

PAGE 

Corona  loss,  effect  of  frequency 129 

effect  of  humidity,  initial  ionization,  etc 147,  148 

effect  of  moisture,  frost,  fog,  sleet,  rain  and  snow. . .    145,  149 

effect  of  smoke  and  wind 149 

effect  of  temperature  and  barometric  pressure 146 

for  small  conductors 136,  137,  140,  142 

harmonics  due  to 118,  207 

law  of 134,  137,  140,  142 

loss  near  the  disruptive  critical  voltage 143 

probability  law 148,  152 

quadratic  law 121 

Corona,  on  generator  coils 216 

Corona  on  transmission  lines,  see  Transmission  lines. 

Corona,  visual,  a.c.  and  d.c appendix,  38,  42,  44,  52,  75 

application  of  electron  theory  to 41,  47,  194 

calculation  for  concentric  cylinder 48,  53,  57,  63 

calculation  of  gradient 40,  42,  47,  53,  63,  67,  71 

calculation  of  voltage 43,  54,  57 

calculation  of  voltage  wet 67,  237 

derivation  of  law  of 49,  53,  63 

diameter  of 74,  78 

effect  of  air  density 42,  51 

effect  of  barometric  pressure 50 

effect  of  cables 43,  71 

effect  of  conductor  material. 43,  44,  46,  48,  68 

effect  of  conductor  surface 43 

effect  of  current  in  conductor , 43,  68 

effect  of  diameter  of  conductor 39,  44,  46,  48 

effect  of  dirt 66 

effect  of  humidity 43,  68 

effect  of  initial  ionization 43,  68 

effect  of  oil 43,  66 

effect  of  small  spacing 42,  57 

effect  of  spacing 39,  44,  45,  46 

effect  of  temperature  on 50,  51 

effect  of  water  on 43,  66,  67 

effect  of  wave  shape 43,  65 

in  CO2  and  H 

influence  of  frequency  on 65 

on  conductors  of  same  potential  close  together 71 

law  of,  for  concentric  cylinder 48,  53,  57,  63 

law  of,  for  parallel  wires 40,  42,  43,  54,  57,  63 

mechanical  vibrations  due  to 78 

photographic  study  of 73 

positive  and  negative 75 

rectifier 76 

stroboscopic  study  of 73 

transient appendix,  108 


INDEX  275 

PAGE 

Cylinders,  concentric,  flux  density 13 

gradient 13,  29 

permittance  or  capacity 13,  29 

visual  corona,  see  Visual  corona 38,  et  seq. 

spark-over  and  corona  in  oil 159 

parallel,  see  Wires. 

D 

Dielectric,  addition  of  fluxes 14 

circuit 215 

displacement 9 

flux  control 35,  223 

flux  density  between  concentric  cylinders 13 

flux  density  between  parallel  planes 11 

flux  density  for  parallel  wires 14,  23 

flux  densities,  sum  of  at  a  point 16,  20 

flux  refraction • 30 

formulae  for  different  electrodes 29 

hysteresis 36,  37 

spark  lag  in  air 108 

spark  lag  in  oil 162 

spark  lag  in  solids 117 

Dielectric  field,  analogy  with  Hooke's  Law 4,  9 

analogy  with  magnetic  field 2 

between  concentric  cylinders 12,  33 

between  parallel  planes 10 

between  parallel  wires 14 

control 223 

energy  stored  in 8,  9,  10 

energy  transfer  in  transmission 8,  9,  10 

equation  of  equipotential  surfaces  between  parallel  wires.  .  .      16 

equation  of  equipotential  surfaces  for  spheres 25 

equation  of  lines  of  force  between  parallel  wires 20 

equation  of  lines  of  force  from  spheres 25 

experimental  determination  of 2,  232 

image  of 234 

in  three  dimensions 232 

methods  of  constructing 226 

resultant 14 

superposition  of 14 

three  phase 238 

Dielectrics,  combination  of  dielectrics  of  different  permittivities 30 

combination  of,  in  multiple 34 

combination  of,  in  series 31 

gaseous 38,  79,  117 

liquid 153 

solid .    166 


276  INDEX 

E 

PAGE 

Elastance, 11,  215 

Elastivity 11,  215 

Electron  theory  application  of,  to  visual  corona 41,  47,  194 

general  discussion  of .• 192 

practical  application  of 194 

Energy  distance 41,  42,  48,  57,  156,  195 

Equipotential  surfaces,  construction  of 226 

equation  of,  for  parallel  wires 16 

equation  of,  for  spheres 25 

in  three  dimensions 232 

Experimental  study  of,  corona  loss 117 

dielectric  fields 2,  232 

solid  insulations 166 

spark-over 79 

strength  of  oil 153 

visual  corona 44 

F 

Flux,  see  Dielectric  flux. 

Frequency,  effect  on  corona  loss 129,  152 

effect  on  visual  corona 65 

see  High  frequency. 

G 

Gamma  rays 193 

Gap,  method  of  measuring  high  voltages 87 

needle 87 

sphere 88 

Green's  theorem 22 

Gradient,  at  any  point 21,  23,  230 

at  different  points  around  a  conductor 231 

between  concentric  cylinders 13,  29 

between  large  spheres 26 

between  parallel  planes 29 

between  parallel  wires 23,  26 

equigradient  surfaces 231,  232 

law  of  visual  corona,  see  Visual  corona 38    et    seq. 

Guard  rings 223 

H 

Harmonics  due  to  corona 118,  207 

High  frequency,  effect  of,  in  design 177,  225 

effect  of,  on  corona  loss 152 


INDEX  277 

PAGE 

High  frequency,  effect  of ,  on  oil 165,  184 

effect  of,  on  solid  insulation 177,  184,  187 

effect  of,  on  spark-over  of  sphere  gaps 105,  106 

loss  in  solid  insulation 187 

Hysteresis,  dielectric 36,  37,  166,  185 


Images 234 

Impulse  ratio 108 

Impulse  voltages,  effect  of,  on  air 108 

effect  of,  on  spark-over  in  oil 162,  165,  187 

effect  of,  on  solid  insulations 177,  184,  187 

measurement  of 108 

Insulation,  breakdown  caused  by  the  addition  of 213 

Insulation,  breakdown,  how  measured 12 

Insulation,  solid,  area  of  electrode 175 

barriers  in  oil 189 

breakdown  caused  by  addition  of ' 213 

common 1 56 

comparison  of  breakdown  in  oil  and  in  air. . .    170    et    seq. 
comparison   of  strengths   for   impulses,    oscillations, 

high  frequency  and  low  frequency 184 

cumulative  effect  of  overvoltages  of  short  duration.  .    178 

d.c.  strength appendix,  191 

effect  of  d.c.  on 191 

effect    of    impulse    voltages     and     high    frequency 

on 177,  184,  187 

energy  loss  in 185 

high  frequency  loss  in 187 

hysteresis 166 

impregnation  of 190 

laminated 175 

law  of  energy  loss  in 185,  187 

law  of  strength  vs.  thickness 174,  237 

law  of  strength  vs.  time 178 

mechanical 190 

methods  of  testing 170  et  seq. 

occluded  air  in 61,  191,  196,  236 

operating  temperatures  of 188 

permittivity  of t .  .  . 179 

resistance 37,  167 

strength  under  high  frequency 184 

strength  under  impulses 177,  184 

strength  under  oscillations 184 

strength  vs.  thickness 174 

strength  vs.  time 178 

tables  of  properties  of 180,  184 


278  INDEX 

PAGE 

Insulations,  air 38,  79   117 

compressed  air 42 

gaseous 38,  79,  117 

liquid 183 

oil 183 

solid 166 

Insulators,  effect  of  altitude  on  spark -over  of Ill 

L 

Lead,  see  Bushing. 

Lines  of  force,  construction  of 226 

equation  of,  between  parallel  wires 18 

equation  of,  for  spheres 25 

equation  of,  three-dimension  field 232 

perpendicular  to  equipotential  surface 20 

Liquid  insulations,  see  Oil. 

M 

Magnetic  field,  analogy  with  dielectric  field 2 

experimental  plot  of .' 2 

N 

Needle  gap 87 

effect  of  humidity  on 88 

spark-over  in  oil 154,  156 

spark-over  voltage  in  rain 105 

O 

Oil,  barriers  in , ! 161,  189 

corona  in 155 

corona  and  spark-over  in 153 

d.c.  strength appendix,  165 

effect  of  moisture  in 154 

effect  of  temperature  on 155 

formulae  for  strength  of '. 159,  161 

high  frequency  in 165 

law  of  spark-over  and  corona > 159,  161 

needle  gap  spark-over  in 156 

permittivity  of 155 

physical  characteristics  of  transil  oil 153 

spark-over  for  different  electrodes  in 154 

specific  resistance  in 155 

surface  leakage  in 188 

transient  voltages  in 162,  184 


INDEX  279 

PAGE 

Oscillations,  effect  of,  on  solid  insulations 177,  184 

effect  of,  on  sphere-gap  voltages 105 

measurements  of 105,  i08 

P 

Paschen's  Law 196 

Permittance  or  capacity,  between  concentric  cylinders 13,  29 

between  concentric  spheres 25 

Permittance  or  capacity,  between  eccentric  spheres 29 

between  parallel  planes 10,  29 

between  parallel  wires 22,  29 

comparison  of  single  phase  and  three  phase . .   235 

effect  of  ground  on  for  parallel  wires 223 

formulae  for  different  electrodes 29 

in  series 12 

Permittivity 11 

of  oil 155 

of  solid  insulations 179 

Planes,  parallel,  flux  density 10,  11 

gradient 10 

permittance  or  capacity  of 10 

spark-over  in  oil 157 

Potential  at  a  point 14 

Potential  difference  between  two  poirfts 14 

Potentials,  addition  of 14 

Problems,  breakdown  caused  by  addition  of  stronger  insulation 213 

bushing 220 

condenser  bushing 220 

dielectric  field  construction  of 226 

dielectric  field  control 223 

dielectric  field  experimental  determination  of 232 

dielectric  field  in  three  dimensions 232 

effect  of  ground  on  dielectric  field  between  parallel  wires .  .  .   234 

entrance  bushings 217 

general  problems  on  the  calculation  of  spark-over  of  parallel 

wires,  insulation  loss,  strength,  etc 236 

graded  cable 218 

high  frequency 225 

static,  on  generator  coils 216 

three-phase  dielectric  field  for  flat  and  triangular  spacings .  .    234 

S 

Spark-over,  at  small  spacings appendix,  63,  93,  196 

condition  for  spark  or  corona 27,  79,  84 

d-c appendix,  107 

effect  of  altitude  on,  for  bushings,  insulators Ill,  217 


280  INDEX 

PAOE 

Spark-over,  effect  of  altitude  on,  for  spheres 95 

effect  of  water  and  rain  on 105 

for  needle  gap 87 

for  parallel  wires 79 

for  spheres . . 88 

gaps  used  in  measuring  high  voltage 87,  88 

influence  of  water  and  oil  on 86 

in  oil 186 

rain  and  wet  on  insulators appendix,  116 

lightning  and  transient appendix,  108,  116 

Specific  resistance,  of  oil 155 

of  solid  insulation 167 

Spheres,  air  films  between 58 

as  a  means  of  measuring  high  voltage 88,  101,  103,  104 

concentric  permittance,  dielectric  field 25 

corona  or  spark-over  for 58 

density  correction  for  air  films appendix,  61,  196 

effect  of  ground  on  spark-over  voltages 104 

effect  of  water  and  rain  on  arc-over  voltages 105 

experimental  determination  of  effect  of  altitude 95 

law  of  disruption 63 

law  of  spark-over  in  air 63 

law  of  spark-over  in  oil 159,  161 

precautions  against  oscillations 101 

rupturing  gradients  for  different  sizes 62 

spark-over  at  high  frequency,  oscillations  and  impulses 108 

spark-over  calculation  of 92,  93 

spark-over  calculation  of,  correction  for  altitude 93 

spark-over  curves • 89  et  seq. 

spark-over  curves  at  small  spacings 60 

strength  of  oil  around 161 

two  large  equal  spheres,  field  between  gradient,  permittance, 

etc 25 

two  small  equal  spheres 28 

Steep  wave  front 105,  108,  162,  177,  184,  187 

Surface  leakage,  air 189,  190,  221 

oil 188 

Symbols,  table  of xiii 

T 

Testing,  method  of  testing  solid  insulations 170  et.  seq. 

Third   harmonic 118,  207 

Three-phase  dielectric  fields  between  conductors  with  flat  and  triangu- 
lar spacings * 238 

Transformer,  bushing 232 

condenser  bushing 220 

oil-filled  bushing 232 


INDEX  281 

PAGE 

Transformer,  voltage  rise  due  to  high  frequency  testing 225 

voltage  rise  due  to  spark-over 102 

Transmission  lines,  agreement  of  calculates  and  measured  corona  losses  208 
corona  limit  of  voltage  on,  with  working  tables.  ...    210 

corona  on 199 

practical  example  of  corona  loss  calculation 205 

practical  formulae  and  their  application 203 

practical  method  of  increasing  size  of  conductors.  .    207 

safe  and  economical  voltages 207 

three-phase,  comparison  of  permittance  with  single- 
phase 234 

three-phase,  with  triangular  and  flat  spacing  .   234,  235 

spark-over  voltage  of 83,  237 

voltage  change  along  lines 208 

U 
Units,  table  of xi 


Visual  corona,  see  Corona. 

W 

Weather,  effect  of,  on  corona  loss 145,  146,  149 

Wires,  calculation  of  spark-over  on,  wet  and  dry 237 

calculation  of  visual  corona  on,  wet  and  dry 237 

corona  loss  on 117,  199,  238 

effect  of  ground  on  permittance  or  capacity  and  gradient 233 

equation  of  equipotential  surfaces 14,  16 

equation  of  lines  of  force 18 

experimental  plot  of  field  between 2,  232 

flux  density 14 

gradient e 23,  29 

law  of  spark-over  and  corona  in  oil 159 

lines  of  force _. .• 14 

method  of  drawing  dielectric  field  for 226 

permittance  or  capacity 22,  29 

spark -over 79 

spark-over,  wet 96 

visual  corona,  see  Visual  corona 38  et  seq. 

X 

X-ravs.  .  .    196 


V- 


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